which expression is equivalent to 4(x-4)

In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

A millimeter, abbreviated mm, is the smallest unit for length in the metric, or Standard International, system of measurement. It is used to measure small lengths and for precise measurements. Millimeters can be converted to either units within the metric system or the customary system of measurement.

Divide 8500 kilometers by which 500 km equals 17.5 millimeters.

Therefore, In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

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The standard deviation of the number of lemons used is equal to 14.7.

Mathematically, the mean for these set of data would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 47 + 45 + 61 + 44 + 16

F(x) = 213.

Mean = 213/5

Mean = 42.6

Next, we would calculate the standard deviation of this data set by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × (47 - 42.6)² + (45 - 42.6)² + (61 - 42.6)² + (44 - 42.6)² + (16 - 42.6)²)

Standard deviation, SD = √(1073.2/5)

Standard deviation, SD = 14.7.

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The function V(r) is representing the volume of basketball when the radius is r.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, the function V(r) =  4/3 πr³, can be used to find the volume of air inside a basketball given its radius (r).

We are asked to find that what does V(r) represents,

Here, V(r) is the function's output is r is the input, the only variable in the formula is r, that means the volume totally depends on the radius of the basket ball. & volume is changes with the radius.

Thus, this function represents the volume of the basketball when radius is r.

Hence, the function V(r) is representing the volume of basketball when the radius is r.

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Answer:

Let the number of $2 notes be x, while that of $10 notes be y.

Set two equations

x + y = 21     y = 21 - x ------- 1

2x + 10y < 110  ------ 2

Sub 1 into 2

2x + 10(21-x) < 110

2x + 210 - 10x < 110

-8x < -100

x > 12.5

Minimum number of $2 notes in the envelope = 13

The percentage of white marbles on the jar is obtained dividing the number of white marbles by the total number of marbles.

A percentage is calculated applying a proportion, dividing the number of total outcomes by the number of desired outcomes, and then multiplying by 100%.

The outcomes for this problem are given as follows:

The problem is incomplete, hence the standard procedure to obtain the percentage of white marbles was presented.

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The function among all options is y=30.5(0.7)ˣ.

The graph of a function represents a set of all points in a plane. It helps to derive the nature of the function.

The function must satisfy the points that are given in the graph.

When x=0, y=21.35(0.7)ˣ=21.35(0.7)⁰=21.35.

But the given point is (0,30.5).

Hence, it cannot be the required function.

When x=0, y=30.5(21.35)ˣ=30.5(21.35)⁰=30.5.

When x=1, y=30.5(21.35)ˣ=30.5(21.35)¹=651.175.

But the given point is (1,21.35).

Hence, it cannot be the required function.

When x=0, y=30.5(1.3)ˣ=30.5(1.3)⁰=30.5.

When x=1, y=30.5(1.3)ˣ=30.5(1.3)¹=39.65

But the given point is (1,21.35).

Hence, it cannot be the required function.

When x=0, y=30.5(0.7)ˣ=30.5(0.7)⁰=30.5.

When x=1, y=30.5(0.7)ˣ=30.5(0.7)¹=21.35.

When x=2, y=30.5(0.7)ˣ=30.5(0.7)²=14.945≈14.95.

It satisfies all three given points.

Therefore, the required function is y=30.5(0.7)ˣ.

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Answer:

Step-by-step explanation:

Given points are P(-1,4) and Q(-4,-2)

we know that slope m between two points (x1,y1) and (x2,y2) is m=y2-y1/x2-x1

so,slope m between points P and Q is m=-2-4/-4-(-1)

m=-6/-3

m=2

Now,we know that equation of line

with slope m having points (x1,y1) and (x2,y2) is y-y1=m(x-x1)

so equation of line between P and Q is y-4=2(x+1)

y-4=2x+ 2

y=2x+6

The number line is completed and attached.

A number line is a straight line that extends in both directions and is used to represent numbers. It is often used to visually demonstrate the relationships between numbers, including ordering and magnitude.

The number line is arranged in steps of 1/4 (fraction) or 0.25 (decimal), this represents the smallest tick marks

The medium sized marks represents the 0.5 line while the largest line mark represents the benchmark numbers chosen suitable to suit the numbers.

The negative part of the number line are numbered with the zero mark.

numbers like 1/8 (or 0.125) are converted to decimal and falls half way between each marked line.

2² = 4 and this is a benchmark number.

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Step-by-step explanation:

The constant in an expression is the number without any letters attached to it.

Looks like B and E are the only ones with constant. The other 3 only have numbers attached to numbers

The blue box measures about 641.667 cm in length.

The width and length of a figure indicate its breadth and length, respectively. The term "breadth" is also used to describe width. Although breadth and width are synonymous (thus the idiom hair's breadth, denoting a very small width), there are two significant differences between the two.

We are aware that the blue box's width is 18 cm, which is smaller than the green box's width (70cm).

As a result, the value of "k" must be lower than 1. By creating a proportion, we can determine the value of "k":

width of green box / width of blue box = k

70 / 18 = k

k = 70/18

k ≈ 3.8889

So the factor "k" is approximately 3.8889. To find the length of the blue box, we can use this factor to scale the length of the green box:

length of blue box = k * length of green box

length of blue box = 3.8889 * 165cm

length of blue box ≈ 641.667cm

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AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.

What is the bisector of the triangle?

The bisector of a triangle is a segment that divides one of its interior angles into two equal parts and continues until it reaches the side opposite that angle. In other words, the bisector of a triangle is a line that divides each interior angle of the triangle into two equal angles.

We have given,

Segment AD is an altitude of ΔABC.

If CD ≅ BD

So, AD is the middle line of the triangle

AD is also an altitude of ΔABC.

So, AD is also an internal bisector of ΔABC

So, AB ≅ AC            ............{Thereom of unity of three lines}

Hence, AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.

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Total hours handled by x judges in the year ≤ 12120x where x is the number of judges needed to handle the caseload for the year.

To formulate an LP for this problem, we can define the decision variables and the objective function and constraints.

Decision Variables:

Let x be the number of judges needed by the city to handle the caseload for the year.

Objective Function:

We want to minimize the number of judges needed, so our objective function is:

minimize x

Constraints:

Each judge can handle up to 120 hours of caseload per month, so the total number of hours that can be handled by x judges in a month is 120x. The total number of hours needed to handle the caseload for the year is given in the table. Therefore, we have the following constraints:

For January: 120x ≥ 100

For February: 120x ≥ 120

For March: 120x ≥ 90

For April: 120x ≥ 80

For May: 120x ≥ 110

For June: 120x ≥ 130

For July: 120x ≥ 140

For August: 120x ≥ 110

For September: 120x ≥ 100

For October: 120x ≥ 90

For November: 120x ≥ 80

For December: 120x ≥ 120

These constraints ensure that the total number of hours handled by the judges in each month is at least as much as the number of hours needed to handle the caseload in that month.

We also need to ensure that all cases are handled by the end of December. This can be expressed as follows:

Total hours handled by x judges in the year ≤ 12120x

This constraint ensures that the total number of hours handled by the judges in the year is less than or equal to the maximum possible number of hours that can be handled by x judges in a year.

Therefore, the LP can be formulated as follows:

minimize x

subject to:

120x ≥ 100

120x ≥ 120

120x ≥ 90

120x ≥ 80

120x ≥ 110

120x ≥ 130

120x ≥ 140

120x ≥ 110

120x ≥ 100

120x ≥ 90

120x ≥ 80

120x ≥ 120

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The value of the ratio (new to original) of the perimeters as required in the task content is; 0.5.

The value of the ratio (new to original) of the perimeters as required in the task content is; 0.25.

Recall, a dilation of a point, (x, y) using a scale factor of k is; (kx, ky).

Also; for shapes A and B;

Perimeter (A) / Perimeter (B) = k.

Also, Area (A) / Area (B) = k².

On this note, since the dilation factor of the pre-image is 0.5, it follows that the ratio of the perimeters of the new to original is; 0.5.

Also, the ratio of the area of the new to original is; 0.5² = 0.25.

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No, we would not expect about 95% of the samples to have their variances within 0.008 of 0.009.

The variance of a normal distribution with mean μ and variance σ^2 is given by σ^2, which in this case is equal to (0.004)^2 = 0.000016.

The variance of the sample means, on the other hand, is given by σ^2/n, where n is the sample size. In order for about 95% of the samples to have variances within 0.008 of 0.009, we would need the sample size to be approximately equal to:

n ≈ σ^2 / (0.008 - 0.009)^2 = 62500

This means that we would need very large samples for this to be true. However, if the sample size is relatively small, then the distribution of sample means will not necessarily be normal and the Central Limit Theorem may not apply.

In that case, the distribution of sample variances will not necessarily follow the same pattern as the distribution of the population variance, and it may not be possible to make predictions about the sample variances based on the population parameters.

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13/16 as a decimal rounded to the nearest tenth is 0.8.

A decimal is a way to represent the same thing but in a different form. In this case, we will convert the fraction 13/16 into a decimal and round it to the nearest tenth.

To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). In this case, 13 divided by 16 is equal to 0.8125. This means that 13/16 as a decimal is 0.8125.

To round a decimal to the nearest tenth, we look at the digit in the hundredths place (the second digit after the decimal point).

If this digit is 5 or greater, we round up the tenths place (the first digit after the decimal point). If it is less than 5, we leave the tenths place as is. In this case, the digit in the hundredths place is 2, which is less than 5.

Therefore, we leave the tenths place as is, and the final answer is 0.8.

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The exact value of sin V in simplest radical form is 0.813.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

Given;

Sin ratio √74:7

Now,

AB/sinA=BC/sinB

√74/sinA = 7/sinB

√74/sin90 = 7/sinB

sinB=7/√74

sinB=0.813

Therefore, the answer of sin V will be 0.813.

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Answer:

The expression is a summation, or the sum of a sequence of terms. Each term is equal to 900 * (1.04)^n+1, where n starts at 1 and goes up to infinity.

To calculate this sum, we would need to find the limit of the sequence as n approaches infinity. However, finding the exact value of this sum is not possible and would require the use of mathematical tools like mathematical analysis.

To estimate the value, we can use a calculator or spreadsheet to calculate the sum for a finite number of terms and then see how the sum changes as we increase the number of terms. For example, if we calculate the sum for n = 1 to 100, we would get an estimate of the value. If we then calculate the sum for n = 1 to 200, we would get a closer estimate.

In this case, we can round the expression to the nearest integer, which would be 53.

Step-by-step explanation:

1. The Venn diagrams are attached

2. When the statistics students number = 10·x + 3, we have;

The number of students that study

When the statistics students number = 2·x + 3, we have;

The number of students that study

The parameters given are;

Total number of students = 30

Number of students that study algebra n(A) = x + 10

Number of students that study statistics n(B) = 10·x + 3

Number of student that study both algebra and statistics n(A∩B) = 4

Number of student that study only algebra n(A\B) = 2·x

Number of students that study neither algebra or statistics n(A∪B)' = 3

Therefore;

The number of students that study either algebra or statistics = n(A∪B)

From set theory we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 10·x + 3 - 4 = 27

11·x+13 = 27 + 4 = 31

11·x = 18

x = 18/11

The number of students that study

a. Algebra

n(A) = 18/11 + 10 = 128/11

b. Statistic

n(B) = 213/11

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11

However, assuming n(B) = (2·x + 3), we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 2·x + 3 - 4 = 27

2·x+3 + x + 10= 27 + 4 = 31

3·x = 18

x = 6

Therefore, the number of students that study

a. Algebra

n(A) = 16

b. Statistics

n(B) = 15

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11

See the attached Venn Diagrams.

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Number of candies that will be left with Jack is 1.375 pounds if the total candies were 5 pounds.

Subtraction can be done for any numbers or algebraic expressions.

It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be called as finding the difference.

Given that,

Total candies that Jack bought = 5 pounds

Candies given to trick or treaters = 3 pounds

Candies left = 5 - 3 = 2 pounds

Amount of candies ate = 10 ounces

16 ounces = 1 pound

10 ounce = 10 / 16 pounds = 0.625 pounds

Amount of candies ate in pounds = 0.625 pounds

Candies left = 2 - 0.625 = 1.375 pounds

Hence the amount of candies left is 1.375 pounds.

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Your question is incomplete. The complete question is given below.

Jack bought 5 pounds of Halloween candy. He gave out 3 pounds of the candy to trick or treaters and ate 10 ounces of the candy. How many ounces of Halloween candy does jack have?

If A, B, and C are n×n invertible matrices, then the solution for "x" in the equation "C⁻¹(A+X)B⁻¹ = Iₙ" is X = BC⁻¹ - A .

The Equation is ⇒ C⁻¹(A+X)B⁻¹ = Iₙ,

We first  multiply both sides by B and C to remove the inverses ;

⇒ C⁻¹(A+X)B⁻¹×BC = I×BC  ;

Simplifying, we get ;

⇒ C⁻¹(A+X)C = B ;

Next, we can multiply both sides by C⁻¹ to separate (A+X) ;

⇒ (A+X)C×C⁻¹= B×C⁻¹  ;

Simplifying, we get:

⇒ (A+X) = BC⁻¹  ;

Now , we subtract "A" from both sides, we get ;

⇒ X = BC⁻¹ - A  ;

So , the solution for X is : X = BC⁻¹ - A  . This solution exists because A, B, and C are all n×n invertible matrices, which means that their inverses exist and the product of invertible matrices is also invertible.

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The given question is incomplete , the complete question is

If A, B, and C are n×n invertible matrices, does the equation C⁻¹(A+X)B⁻¹ = Iₙ have a solution, X ? If so, find it.

Answer: MHT = 125; AHM = 55

Step-by-step explanation:

(2x + 11) + (6x - 7) = 180 since they are supplementary angles

8x + 4 = 180 ---- subtract 4 on both sides

8x = 176 ---- divide by 8 on both sides

x = 22

MHT = 6x - 7

6(22) - 7 = 132 - 7 = 125

AHM = 2x + 11

2(22) + 11 = 44 + 11 = 55

The probability that the committee has exactly two woman is 0.1758.

Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.The ratio of the favorable outcomes to the all possible outcomes.

Given that, 4 women and 5 men are eligible to serve on a committee.

A committee of 3 is randomly selected.

Choosing 2 women out of 3 women is

³[tex]C_{2}[/tex]

= 3

Choosing 1 men out of  5 men is

5C1

= 5

Total number of eligible person is = (4+5)=9

Choosing 3 member out of 9 member is

9C3

=84

The required  probability is

=3*5/84

0.1785

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Answer: look at the image for the answer and the solution

Step-by-step explanation:

Answer: the home of it is 78 degrees

Step-by-step explanation:

as the angular bisector is shown then we can say that its right

Answer: the perimeter of the polygon is 29cm

Step-by-step explanation:

Answer:

x + y = -6

Step-by-step explanation:

Just put x and y and add the number on the RHS
Its really not that hard

But i hope it helped

Answer: x=3

Step-by-step explanation:

4x-3y=18

4x-3(-2)=18

4x+6=18

(4x=12)/4

x=3

Answer:

Step-by-step explanation:

If you are implying that the equation is "6x = 60"

Divide both sides by 6 to get just x by itself, then you'd have your answer.

X  = 10

Answer:

None

Step-by-step explanation:

The reason is because none of them add up to at least 91°

62° would be your best bet but, even when you do the math 62*2= 124

124/6= 20 2/3°

62+20.66...= 82.666...

82.6666...<91°

Answer:

70%

Step-by-step explanation:

The graph is wrong because of less than or equal to sign. the correct inequality for the given graph would be y ≥ 3x - 2.

What is inequality?

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

The given graph is wrong for the given inequality  y ≤ 3x - 2

The correct graph for the given inequality is shown below.

The given graph would be correct for the inequality

y ≥ 3x - 2.

Hence, the graph is wrong because of less than or equal to sign. the correct inequality for the given graph would be y ≥ 3x - 2.

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