What is y=-6x+2 in standard form

    Given ,

To Find : Maximum number of small cube shaped boxes that can fit in the cuboid

Volume of the Cuboid = [tex]2(lb+bh+lh)[/tex]

Volume of the cuboid = [tex]2(70X40+40X40+70X40)[/tex]

                                      = [tex]14400cm^{3}[/tex]

Now to find the volume of a cube,

[tex]V = a^{3}[/tex]

[tex]V = 10X10X10[/tex]

[tex]V = 1000cm^{3}[/tex]

Number of boxes that can fit in a cuboid = [tex]\frac{14400}{1000}[/tex]

                                                                    = [tex]14boxes[/tex]

Hence , the number of cube shaped boxes that can fit in a cuboid are 14

Experimental probablity will be - 12 over 30

Answer: D: 12/60 (12 over 60)

Step-by-step explanation:

Since the circumference of the base is given, the radius can be calculated as r = (circumference / 2π) and the volume as V = πr2h. The volume of the cylinder is therefore approximately 628.3 cubic centimeters.

1. Calculate the radius of the base of the cylinder. The circumference of the base is 167 centimeters. Rearranging this gives

r = C / 2π. Therefore,

r = (167 / 2π)

= 26.6 cm.

2. Calculate the volume of the cylinder. The formula for volume is V = πr2h. Therefore,

V = π(26.6)2 * 5

= 628.3 cubic centimeters.

or

r = (167 / 2π) = 26.6 cm

V = π(26.6)2 * 5 = 628.3 cubic centimeters

To calculate the volume of the cylinder, the radius of the base must first be calculated. This can be found by using the formula C = 2πr, where C is the circumference and r is the radius The circumference of the base of the cylinder is 167 centimeters, so the radius can be calculated as r = (167 / 2π) = 26.6 cm. The volume of the cylinder can then be calculated using the formula V = πr2h, where h is the height of the cylinder. In this case, the height is 5 centimeters, so the volume is V = π(26.6)2 * 5 = 628.3 cubic centimeters. This is the closest measurement to the volume of the cylinder.

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The linear equation f(x) is  4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.

The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:

m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4

The y-intercept (b) can be found using one of the points and the slope:

b = y - mx = 2 - 4(3) = -10

So the linear equation in standard form is:

f(x) = 4x - 10

For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.

Let's (3,2) point 1 and (7,18) point 2.

f(k) = ak^2 + bk + c....(1)

point 1: f(3) = 2 = 9a + 3b + c...(2)

point 2: f(7) = 18 = 49a + 7b + c...(3)

Now we have 2 equations and 3 unknowns.

using theirs first equation and substitute it in the second and third equation

18 = 49a + 7b + c

2 = 9a + 3b + c

c = 2 - 9a - 3b

18 = 49a + 7b + (2 - 9a - 3b)

18 = 49a + 7b + 2 - 9a - 3b

18 = 40a + 4b + 2

16 = 40a + 4b

now this equation is used to solve for a and b

b = (16 - 40a) / 4

so a,b and c are

a = -5/2

b = 4

c = -1

so the quadratic equation in standard form is:

f(k) = -5/2k^2 + 4k - 1

4x - 10 is the linear equation f(x)  and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.

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Answer:

Yolanda's answer is incorrect because the recipe calls for 1 cup of almonds, 1 cup of pecans, and 1 cup of dried fruit, which totals 3 cups of nuts. The correct ratio of nuts to fruit in this recipe is 3:1. This means that for every 3 cups of nuts, there is 1 cup of fruit.

The equation the line is, y-3x=1

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (-1,-2) and, (3,10)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y+2)/(x+1)=(10+2)/(3+1)

=>y+2=3x+3

=>y-3x=1

Hence, the required equation is,  y-3x=1

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Answer:

$8

Step-by-step explanation:

For a trigonometric equation. Cos^2x=3sin^2x, the solution is mathematically given as x = π/6 + 2nπ.

Trigonometry is the study of angles and the angular connections of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

Generally, the equation for the trigonometric equation is mathematically given as:

Cos^2x=3sin^2x

Therefore

1 - sin^2(x) = 3 sin^2(x)

1/4 = sin^2(x)

Hence introducing \pi

x = arcsin(1/2) + 2nπ  

x = π/6 + 2nπ

In conclusion,

x = π/6 + 2nπ

For a trigonometric equation. Cos^2x=3sin^2x, the solution is mathematically given as x = π/6 + 2nπ.

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Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

Given :

At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.

after traveling six blocks at her normal speed of three blocks per minute

She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.

She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).

Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

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The mean, variance, and standard deviation for the probability distribution given are A. Mean = 5.5; B. Variance = 13.875; C. Standard Deviation = 3.722.

The mean, variance and standard deviation of the probability distribution can be calculated using the formula. The mean is calculated by summing up the product of all the values and their respective probabilities and then dividing it by the total probability. In this case, the mean is calculated as:

(1*0.587 + 3*0.115 + 9*0.21 + 12*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 5.5.

The variance is calculated by summing up the product of the squares of the values and their respective probabilities and then dividing it by the total probability. In this case, the variance is calculated as:

(1^2*0.587 + 3^2*0.115 + 9^2*0.21 + 12^2*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 13.875.

The standard deviation is the square root of the variance and it is calculated as √13.875 = 3.722.

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The length of the side of the table top as calculated from the given data will be 6x⁴y².

To calculate the area of the table top we will have to square of the sides given .

area =(36x.16y^4 )²

side =√(36x.16y^4 )²

= 6x⁴y².

In mathematics the product of a number multiplied by itself is considered to be its square. Eg.) 6 multiplied by 6 gives 36 which is known as its square.

The given table is square in shape and hence its area will be given my multiplying its side with itself.

Area of a square = side x side.

To find its length we can simply find the square root of the number.

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Answer: $95.76

Step-by-step explanation:

If the 15 is referencing 15%.

15% of 638.40 can be found by making 15% a decimal by moving the decimal to the left twice.

.15 X 638.40= 95.76

The total amount in the bank after the specific number of years is;

9.  $476. 1

11. $7, 128. 8

The formula for calculating simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

9.Principal amount = $450

Interest rate = 1.45

Time = 5

Substitute the values into the formula

SImple interest = $450 ×1. 45× 5/100

Multiply the values, we get;

Simple interest, I = 2610/100

Divide through

Simple interest = $26. 1

Total amount = $450 + $26.1 = $476. 1

11. Principal amount = $5600

Interest rate = 3.9

Time = 7 years

Substitute the values

Simple interest = $5600× 3. 9 × 7/100

Multiply the values

Simple interest = 152,880/100

Simple interest = $1528. 8

Total amount = $7, 128. 8

Hence, the values are $476. 1 and  $7, 128. 8

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The volume of a right square pyramid PABCD is 50.91 cubic units

Let l be the side length of right squared pyramid and h be the height.

We know that the formula for the volume of the right squared pyramid.

V = a²h / 3

And the formula for the height of right squared pyramid.

h = (1/√2)a

Here, the side length (a) = 6 units

So, using above formula of height,

h = (1/√2) × 6

h = 6/√2

h = 3√2 units

Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,

V = (6² × 3√2) / 3

V = 6² × √2

V = 36√2

V = 50.91 cubic units

Therefore, the volume of PABCD is 50.91 cubic units

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this question is related to numbers and the solution is as follows,

Rover eats 3/4 can of cat food in a day.

given

in 60 days it will consume 60 x 3/4 cans = 45 cans of cat food

3 cans cost = $5 and a pack contains 3 cans

45 cans is equivalent to= 45/3

= 15 packs

15 packs cost = 15 x $5 = $75

So it will cost $ 75 to feed Rover for 60 days

Bobo eats 1/2 of a can of cat food per day

in 60 days it will consume 60 x 1/2 cans = 30 cans of cat food

3 cans cost $5 and a pack contains 3 cans

30 cans are equivalent to 30/3 = 10 packs

10 packs will cost = 10 x $5 = $50

So it will cost $50 to feed Bobo for 60 days

In total, in 60 days it will cost $75 +$ 50 = $125 to feed both cats in 60 days.

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As calculated from the data we get the result as that $ 125 is required for the cat food of both the cats in a month.

We are given that in 60 days he will consume  ,

60 x 3/4 cans

= 45 cans of cat food

The cost of 3 cans cost = $5

and one pack has 3 cans in it.

Therefore, 45 cans is equivalent to

= 45/3

= 15 packs

So , the cost of 15 cans will be ,

15 packs cost = 15 x $5 = $75

Therefore ,$75 is used for 60 days of cat food for Rover.

Now , we know that Bobo eats 1/2 of a can food in a day.

Therefore, in 60 days he will  eat,

60 x 1/2 cans

= 30 cans of food

As we know, 3 cans cost $5 and a pack contains 3 cans

Therefore, 30 cans = 30/3 = 10 packs

10 packs will cost = 10 x $5 = $50

So , $50 is spend to feed Bobo , in a month.

Therefore , if will combine their cost we will get that ,

$75 +$ 50 = $125 is required to feed both the cats in one month.

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The transformation of S(1,-4), R(2,0), 2(3,0), and P(3,-2) is S(-6, -2), R(-6, 2), as well as the category is rotation transformation.

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image, which refers to the object's initial shape, and the Image, which refers to the object's ultimate shape and location after transformation, are both terms. Transformations can be divided into three categories: translations, reflections, and dilations. There are two types of transformations that can be done to a function: vertical (which affects the y-values) and horizontal (affects the x-values). The four transformation variables are included in the equation of a function that is shown below (a, b, h, and k). changing the log. Take the log of every observation as an example. Transposition by the square root. The square root of each observation is what is need for this.

given

Translation or shift vector refers to the pair (tx, ty). Column vectors are another way to visualize the aforementioned equations.

S(1,-4), R(2,0), 2(3,0), P(3,-2) to S'(-5,-2), R'(-4, 2), Q'(-3, 2), P(-3,0)

is S (-6, -2) , R( -6 , 2)

The transformation of S(1,-4), R(2,0), 2(3,0), and P(3,-2) is S(-6, -2), R(-6, 2), as well as the category is rotation transformation.

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On solving the provided question, we can say that - the volume of the cylinder will be V = 3.14 * 20*20*50 = 62800

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter

volume of the cylinder -

V = [tex]\pi r^2h[/tex]

r = 40/2 = 20

h = 50

V = 3.14 * 20*20*50 = 62800

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The mirror image of (2,5) in y-axis is (-2,5)

The term mirror image of the point is a reflected duplication that appears identical but in reverse.

Here we have given point is (2, 5).

And we have to find the mirror image of this point with respect to the y-axis that is the mirror image is a point whose distance is same from the origin O (0, 0) and same from both axes as of the point (2, 5) is.

As we all know that (2, 5) lies on the first quadrant, then the mirror image with respect to the y-axis must lie on the second quadrant.

And we all also know that In second quadrant, here the x-coordinate of any point (x, y) is negative.

Therefore, while we looking into the given graph we have identified that the mirror image is (- 2, 5).

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Answer:

the answer is a

and the correct answer is letter C

Step-by-step explanation:

I don't know that is the answer

Answer:

2

When you cancel out the m (cause its the common factor) the only thing left is to simplify 10/5 which is 2.

Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

On solving the provided question, we can say that - the value ox in the following angle = 3x = 84 => x = 28

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.

here

angle JMP = 3x-6 - 90

3x = 84

x = 28

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Recently, the Town of Aberdeen announced they were going to acquire a large parcel of land for a new park initiative.

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Answer:

a. 1.6

b. 16

c. 0.16

d. 1.6

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, Manuel says [tex]25\frac{5}{8}[/tex] feet of fencing is enough for a rectangular flower bed that measures [tex]9\frac{7}{8}[/tex] feet by [tex]15\frac{3}{4}[/tex] feet

Here, perimeter =2([tex]9\frac{7}{8}[/tex] +  [tex]15\frac{3}{4}[/tex]) feet

= 2(79/8 + 63/4)

= 2(79/8 + 126/8)

= 2(205/8)

= 410/8

= [tex]51\frac{1}{4}[/tex] feet

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

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Answer:

[tex]v=-18,14[/tex]

Step-by-step explanation:

[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]

If their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

The term taxable income refers to any gross income earned that is used to calculate the amount of tax you owe. Put simply, it is your adjusted gross income less any deductions. This includes any wages, tips, salaries, and bonuses from employers.

The minimum income amount depends on your filing status and age. In 2022, for example, the minimum for single filing status if under age 65 is $12,950. If your income is below that threshold, you generally do not need to file a federal tax return. Review the full list below for other filing statuses and ages.

Taxable income

a. Taxable income:

Taxable income=Gross income - Total taxes due

Taxable income=$63,000-$6,847.50

Taxable income=$56,152.5

b. The marginal tax rate for taxable income  under the income bracket of of $40,526 to $86,375 is 22%.

c. Effective tax rate:

Effective tax rate = Total taxes due/ Taxable income×100

Effective tax rate =$6,847.50/$56,152.5×100

Effective tax rate =10.869%

Effective tax rate =10.87% (Approximately)

Inconclusion if their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

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There is very strong evidence to reject the null hypothesis, and to conclude that the machine gives radiation doses lower than the maximum on the label.

Hypothesis testing is a statistical method used to test a claim or a hypothesis about a population parameter, based on a sample of data. The goal of hypothesis testing is to determine whether there is enough evidence in the sample data to support or reject a claim about a population.

A t-test is a type of statistical hypothesis test that compares the mean of a sample to a known population mean. There are different types of t-tests, depending on the design of the study and the number of samples being compared.

To test the claim that the machine gives a radiation dose lower than the maximum on the label (5.00 milliroentgens), we can use a one-sample t-test. A one-sample t-test compares the mean of a sample to a known population mean (in this case, the maximum on the label). The null hypothesis for this test is that the mean radiation dose given by the machine is equal to or greater than the maximum on the label (5.00 milliroentgens). The alternative hypothesis is that the mean radiation dose given by the machine is less than the maximum on the label.

The test statistic for a one-sample t-test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values:

t = (4.23 - 5.00) / (1.91 / sqrt(46)) = -4.05

We can use a t-distribution table to find the p-value associated with this test statistic. With 45 degrees of freedom (sample size - 1), the p-value for t = -4.05 is extremely low, much less than 0.001, the significance level commonly used in hypothesis testing.

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We can see here that the effect that the circled point will have on the y-intercept is: B. The y-intercept will decrease because the point pulls the least-squares regression line toward it.

In statistics, an intercept is the value of the dependent variable when the independent variable(s) is equal to zero. It is often represented by the symbol "b" in a linear equation.

For example, a simple linear equation has the form y = mx + b, where "y" is the dependent variable, "x" is the independent variable, "m" is the slope of the line, and "b" is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

We see here that the answer above is the correct answer.

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The equation is x + 0.3 = 9.124 and the value of x is 8.824.

The following is a linear equation in one variable. It can be expressed in the form of ax+b=0. Here a and b are integers and x is a variable that has only one solution. In these type of equations only one variable is present.

We can write an equation to find the score without the penalty by using the information provided. Let x be the score without the penalty. We know that the final score (with the penalty) is 9.124 and that the penalty is 0.3 points. Therefore, we can set up the equation:

x + 0.3 = 9.124

To find the score without the penalty, we need to subtract 0.3 from both sides of the equation:

x = 9.124 - 0.3

x = 8.824

So, the score without the penalty is 8.824

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