A factor goes into a larger number _____.

Answer:

a) 15, 25

Step-by-step explanation:

Finding the average is to find the sum and divide it by the quantity of the numbers.

(15 + 25) / 2 = 40 / 2 = 20, 20 is the average of two numbers.

However standard deviation includes at least one degree of 2.

x1 + x2 = 40

SD = 5

= [tex]\sqrt{[(x_1 - 20)^2 + (x_2 - 20)^2]/2 \\}= 5\\ x_1 = 15, or x_1 = 25\\x_2 = 15 or x_2 = 25[/tex]

Answer:

the present value that must be invested to have a future value of $6000 after 6 months at a simple interest rate of 1.45% is approximately $5957.00.

Step-by-step explanation:

To determine the present value P that must be invested to have a future value A at a simple interest rate r after time t, we use the formula:

A = P (1+r)^t

P = A / (1+r)^t

where P is the present value, A is the future value, r is the simple interest rate as a decimal, and t is the time period in years.

In this case, the future value is $6000, the simple interest rate is 1.45% or 0.0145 as a decimal, and the time period is 6 months or 0.5 years.

Substituting these values into the formula, we get:

P = 6000 / (1+0.0145)^0.5 = 5,957.00

= $5957.00 (rounded to two decimal places)

Therefore, the present value that must be invested to have a future value of $6000 after 6 months at a simple interest rate of 1.45% is approximately $5957.00.

The present value P to be invested can be calculated using the reverse of the simple interest formula A = P * (1 + r * t). Given A = $6000, r = 1.45%, and t = 6 months, we can find P by rearranging the formula to P = A / (1 + r * t) and substituting the given values.

To calculate the present value P, which needs to be invested under simple interest to amount to a future value A, we use the formula for simple interest in reverse. The formula is:

A = P * (1 + r * t)

Re-arranging for P:

P = A / (1 + r * t)

where,

Given that A = $6000, r = 1.45% = 0.0145 (per year), and t = 6 months = 0.5 years, the present value P can be calculated as:

P = 6000 / (1 + 0.0145 * 0.5)

Calculate the above expression to determine P.

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The measures of the angles in the parallel lines is

m∠a = 97°

m∠b = 15°

m∠c = 68°

m∠d = 68°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the two parallel lines be represented as l and m

Now , the transversal line is t

The measure of m∠a = 97° ( corresponding angles )

The measure of m∠d = 180° - 112° ( angles in a straight line = 180° )

So , the measure of m∠d = 68°

The measure of m∠c = measure of m∠d ( alternate interior angles )

So , the measure of m∠c = 68°

From the triangle formed by the intersection of lines ,

The measure of m∠b = 180° - ( a + d ) ( angles of a triangle = 180° )

So , the measure of m∠b = 180° - ( 97° + 68° )

The measure of m∠b = 15°

Hence , the measures of angles are solved

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Proof for the given statement is given below.

Vertical angles are the angles formed on two opposite sides of intersecting lines.

The measure of a pair of vertical angles are equal.

Given are two line segments intersected each other.

The line segments are KM and JN.

Consider ΔJKL and ΔLMN.

Given JL / NL = KL / ML

This means that two corresponding sides of ΔJKL and ΔLMN are proportional.

In a similar triangles, corresponding angles are equal.

So they are similar triangles.

∠JLK and ∠MLN are a pair of vertical angles.

So they are equal.

Corresponding angle of J in ΔJKL is angle N in ΔLMN.

So ∠J = ∠N

Or, ∠J ≅ ∠N

Hence it is proved.

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The number that can be placed in the blank to make the number sentence true is given as follows:

1/316.

The number sentence for this problem is given as follows:

"316 times which number equals 1".

The number is unknown, hence the variable that represents the number is given as follows:

x.

The times word means a multiplication operation, hence the expression is given as follows:

316x = 1.

Now we must simply solve the expression 316x = 1 for the variable x, applying the division, which is the inverse operation of the multiplication, hence:

x = 1/316.

Which is the number that satisfies the number sentence.

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Answer:

x = 229

Step-by-step explanation:

x = 467 - 238

x = 229

The histogram has a longer right tail since skewed right side

The distribution of data is positively skewed distribution

A histogram with a longer right tail indicates that the data is skewed to the right, which means that the majority of the data points are on the left side of the graph, and there are fewer data points on the right side. This is also known as a positively skewed distribution.

In a positively skewed distribution, the mean is typically greater than the median, and the mode is less than the median. This is because the presence of outliers on the right side of the graph can pull the mean towards higher values, while the median remains closer to the bulk of the data.

The graph that represents this is D.

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The minimum score Chen can earn on the final test to get at least 80 percentage avg. on the tests is 41.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

As a percentage, "%" is read as "percent" or "percentage" in this context. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".

Now in the given question,

Chen has total no of tests = 4

Total marks of the tests = 4 × 50 (Each test is worth 50 points)

= 200 marks.

So, to secure at least 80% average Chen has to score:

80% of 200

= 80/100 × 200

= 80 × 200/100

= 160

Now Chen has already secured 45, 38 and 36 points in 3 tests.

So, the points he has to secure in the last test =

160 - 45+ 38 + 36

= 41

Therefore, the minimum score Chen can earn on the final test to get at least 80% avg. on the tests is 41.

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The actual value of cos θ is -(51)/10 based on the information provided.

Noun. Values in plural. Definition of value from the Britannica dictionary. 1.: the monetary value of something, often known as its price or cost.

The Pythagorean identity can be used to determine the value of cos θ if sin θ = 7/10 and is θ in quadrant II:

cos² θ + sin² θ = 1

cos² θ + (7/10)² = 1

cos² θ + 49/100 = 1

cos² θ = 51/100

cos θ = ±√(51/100)

Since θ is in quadrant II, cos θ is negative. Therefore,

cos θ = -√(51/100)

Putting it more briefly,

cos θ = -(√51)/10

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Answer:

a=50-40

a=10

lxb

answer

Answer:

29n - 39/2.

Step-by-step explanation:

To simplify the expression 8(3n-2) + 1/2 (10n-7), we can start by using the distributive property of multiplication over addition to simplify the terms inside the parentheses:

8(3n-2) + 1/2 (10n-7) = (83n - 82) + (1/2 * 10n - 1/2 * 7)

This gives us:

24n - 16 + 5n - 7/2

Next, we can combine like terms:

24n + 5n - 16 - 7/2 = 29n - 16 - 7/2

Finally, we can simplify the expression by finding a common denominator for -16 and -7/2:

29n - 16 - 7/2 = 29n - 32/2 - 7/2 = 29n - 39/2

Therefore, 8(3n-2) + 1/2 (10n-7) simplifies to 29n - 39/2.

As a result, x = pi/6 is the only answer in the range [0,2pi).

When quantifying the angles of trigonometry or periodic functions, radians are frequently taken into account. Radians are always expressed in units of pi, with pi equivalent to either 3.14 or 22/7.

We can start by simplifying the left-hand side of the equation using the identity:

csc x = 1/sin x

4 sec x csc x = 4(1/cos x)(1/sin x) = 4/(cos x sin x)

Substituting this back into the original equation, we get:

4/(cos x sin x) = 8 csc x

Multiplying both sides by cos x sin x, we get:

4 = 8 sin x

Dividing both sides by 8, we get:

sin x = 1/2

This means that x is either pi/6 or 5pi/6, since these are the two angles in the interval [0,2pi) where sin x = 1/2.

However, we need to check if these solutions satisfy the original equation.

For x = pi/6:

4 sec x csc x = 4 sec(pi/6) csc(pi/6) = 4(2) (2/√3) = 16/√3

8 csc x = 8 csc(pi/6) = 8(2/√3) = 16/√3

So, x = pi/6 is a solution.

For x = 5pi/6:

4 sec x csc x = 4 sec(5pi/6) csc(5pi/6) = 4(-2) (-2/√3) = 16/√3

8 csc x = 8 csc(5pi/6) = 8(-2/√3) = -16/√3

So, x = 5pi/6 is not a solution.

Therefore, the only solution in the interval [0,2pi) is x = pi/6.

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If you are considering taking out a loan against the value of your home equity, there are several options to consider. One of the most common types of home loans for this purpose is a home equity loan or a home equity line of credit (HELOC).

The difference between the value of your home and the amount you owe on your mortgage is known as Home equity.

A home equity loan is a lump sum loan that allows you to borrow against the equity in your home. You receive the funds in one lump sum and then make fixed monthly payments over a set period of time, typically 5-15 years.

The interest rate on a home equity loan is generally fixed, which means that your monthly payments will remain the same throughout the life of the loan.

With a HELOC, you have access to a revolving line of credit, much like a credit card, and you only pay interest on the amount you borrow. The interest rate on a HELOC is typically variable, which means that your monthly payments may fluctuate over time.

Both home equity loans and HELOCs may make sense for helping your sister through a rough patch, as they can provide you with access to cash quickly and may offer lower interest rates than other types of loans. However, it's important to remember that both of these loans are secured by your home, which means that if you are unable to make your payments, you risk losing your home.

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Answer:

The triangle is acute.

Step-by-step explanation:

To determine whether the side lengths of 3, 7, and 9 can form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this condition is satisfied for the given side lengths:

3 + 7 = 10 > 9, so the sum of the two smaller sides is greater than the largest side.

7 + 9 = 16 > 3, so the sum of the two smaller sides is greater than the largest side.

3 + 9 = 12 > 7, so the sum of the two smaller sides is greater than the largest side.

Since all three inequalities are true, we can conclude that the given side lengths of 3, 7, and 9 can form a triangle.

To determine whether the triangle is acute, right, or obtuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's first determine which side is the longest. Since 9 is the largest side length, it must be the hypotenuse if the triangle is right-angled.

However, using the Pythagorean theorem, we can see that:

3^2 + 7^2 = 58 < 9^2, so the triangle is not right-angled.

Therefore, the triangle must be either acute or obtuse. To determine which one, we can use the law of cosines, which states that in any triangle:

c^2 = a^2 + b^2 - 2ab*cos(C)

where a, b, and c are the side lengths, and C is the angle opposite to side c.

Let's apply this formula to the triangle with side lengths 3, 7, and 9:

9^2 = 3^2 + 7^2 - 2(3)(7)*cos(C)

81 = 58 - 42*cos(C)

cos(C) = (58 - 81)/(-42) = 0.5476

C = cos^(-1)(0.5476) = 56.69 degrees

Therefore, the largest angle in the triangle is approximately 56.69 degrees. Since this angle is less than 90 degrees, we can conclude that the triangle is acute.

Answer:

obtuse angled triangle

Step-by-step explanation:

for the sides to form a triangle

the sum of any 2 sides must be greater than the third side.

3 + 7 = 10 > 9

3 + 9 = 12 > 7

7 + 9 = 16 > 3

then the 3 sides 3 , 7 , 9 will form a triangle

given 3 sides a , b , c with c the longest side

• if a² + b² = c² ⇒ right triangle

• if a² + b² > c² ⇒ acute angled triangle

• if a² + b² < c² ⇒ obtuse angled triangle

here a = 3 , b = 7 , c = 9

a² + b² = 3² + 7² = 9 + 49 = 58

c² = 9² = 81

since a² + b² < c²

then triangle is obtuse

The required maximum point of the function [tex]$f(x)=-x^2+8x+40$[/tex] is (4,24).

A quadratic equation is an algebraic equation with a maximum degree of two. Where a 0, the equation is provided by ax² + bx + c = 0.

To find the maximum point of the quadratic function [tex]$f(x)=-x^2+8x+40$[/tex], we can use the formula for the x-coordinate of the vertex, which is given by [tex]x=-\frac{b}{2a}$[/tex], where a is the coefficient of the [tex]x^2$[/tex] term and b is the coefficient of the x term.

In this case, a=-1 and b=8, so the x-coordinate of the vertex is:

[tex]$x=-\frac{b}{2a}=-\frac{8}{2(-1)}=4$$[/tex]

To find the y-coordinate of the vertex, we can plug this value of x into the original function:

[tex]$$f(4)=-4^2+8(4)+40=24$$[/tex]

Therefore, the maximum point of the function [tex]$f(x)=-x^2+8x+40$[/tex] is (4,24).

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The charge for the third company for the 8 feet of copper pipe as required to be determined is; $8.50.

As evident from the task content;

For the first company; Pipe for $1.50 per foot and a rebate offering $2.00 off the total.

Therefore, total charge is; 8(1.50) - 2 = $10.

For the second company; Pipe for $1.75 per foot and a coupon offering $0.25 off each foot.

Therefore, total charge is 8(1.75) - 8(0.25) = $12.

Hence, since the better deal is; $10.

Ultimately, the charge of the third company whose offer is; $1.50 less than the charge of the better deal is; 10 - 1.50 = $8.50.

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Step-by-step explanation:

To find the maximum height of the object, we need to determine the vertex of the parabolic function f(t) = 16t^2 + 16t + 7.

The vertex of a parabola in the form f(t) = at^2 + bt + c is given by (-b/2a, f(-b/2a)). In this case, a = 16, b = 16, and c = 7, so the vertex is:

(-b/2a, f(-b/2a)) = (-16/(216), f(-16/(216))) = (-1/2, f(-1/2))

To find f(-1/2), we can substitute t = -1/2 into the function:

f(-1/2) = 16(-1/2)^2 + 16(-1/2) + 7 = 8 - 8 + 7 = 7

Therefore, the vertex is at (-1/2, 7). This means that the maximum height of the object is 7 feet above the ground.

Alternatively, we could also use the fact that the maximum height occurs at the vertex of the parabola, which is the point where the derivative of the function is zero. The derivative of f(t) is:

f'(t) = 32t + 16

Setting this equal to zero and solving for t, we get:

32t + 16 = 0

t = -1/2

So the maximum height occurs at t = -1/2, which corresponds to the vertex of the parabola, and the maximum height is 7 feet.

Therefore, the estimated mean is roughly 0.154, but without more data, we are unable to calculate the SEM or group size.

The total of all values divided by all of the values constitutes the result of a set, also called as the arithmetic mean. It is considered to be the most popular central trend indicator, and the word "mean" is commonly used to describe it. multiply the total amount of numbers in the library by the overall amount of values inside the gathering to get this result. Either original data or data that's been combined into frequency charts can be used for calculations. The average of a figure is known to as the average.

Here,

Given a normal distribution, the MAD and standard deviation (SD) are roughly inversely proportional to one another as follows:

=> MAD = 1.4826 × SD

As a result, we can calculate the standard deviation as follows:

=> SD = MAD / 1.4826

Since the MAD in this instance is provided as 3.2, we can calculate the standard deviation as follows:

=> SD ≈ 3.2 / 1.4826 ≈ 2.16

The standard error of the mean (SEM), which can be determined as follows, then provides the variability of the mean.

=> SEM ≈ SD / sqrt(n)

=> CV Equals SD/mean

To find the mean, we can change this equation as follows:

a) Mean Equals SD / CV

With the estimated numbers for SD and CV substituted, we obtain:

=> mean ≈ 2.16 / 14 ≈ 0.154

Therefore, the estimated mean is roughly 0.154, but without more data, we are unable to calculate the SEM or group size.

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Answer:

Step-by-step explanation:

Line 1: (2 - 7)/(-2 + 4) = -5/2

Line 2: (-1 + 8)/(0 + 5) = 7/5

Line 3: (8 + 2)/(-2 -2)= 10/-4 = -10/4 = -5/2

Line 1 and Line 2: Neither

Line 1 and Line 3: Parallel

Line 2 and Line 3: Neither

Answer:

Step-by-step explanation: The equation should be

A = 35 - 4t

B = 50 - 7t

And, the Height = 15 inches

Calculation of the equation and height;

Since

Height of snowman A = 35 inches

Height of snowman B = 50 inches

Height decrease of snowman A = 4 inches per hour

Height decrease of snowman B = 7 inches per hour

Here, t = number of hours

So, the equation should be

A = 35 - 4t      

B = 50 - 7t      

Now for the same height

35 - 4t = 50 - 7t

-4t + 7t = 50 - 35

3t = 15

t = 15

So,

A = 35 - 4(5) = 35 - 20 = 15 inches

B = 50 - 7(5) = 50 - 35 = 15 inches

The angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

We shall evaluate for the angle of elevation θ in degree, and then convert the result to radian as follows:

θ = tan⁻¹(4255/2000)

θ = 64.82482°

we multiply by π/180 to convert to radian;

θ' = 64.82482° × π/180

θ' = 1.13186 rounded to five decimal place.

Therefore, the angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.

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The lengths DG and GC are 12 and 24 units respectively

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

G is the centroid and DC = 36.

The centrod divides the triangle in 1 : 2

Using the above as a guide, we have the following:

DG : GC = 1 : 2

Multiply by 12

So, we have

DG : GC = 12 : 24

12 and 24 add uo to 36

This means that

DG = 12 and GC = 24

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The rectangle has a surface area of 6 1/4 squares.

The territory a rectangle occupies inside its 4 corners or limits is referred to as its area. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

The amount of space within a form is measured by its area. In daily life, figuring out a shape's or surface's area can be helpful. For instance, you may require know how so much paints to buy to paint a board or the amount of grass to plant on a lawn.

To find the area,

[tex]Area=lenght*width[/tex]

[tex]Area=\frac{5}{2} *\frac{5}{2}[/tex]

[tex]Area=\frac{25}{4}[/tex]

[tex]Area=6\frac{1}{4} square unit[/tex]

Therefore, the area of the rectangle is [tex]Area=6\frac{1}{4} square unit[/tex]

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The answer of the given question based on the cost of mailing is , the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

An equation is  mathematical statement that shows  two expressions are equal. It contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, and division.

For example, a simple equation could be:

2x + 3 = 9

The equation y = 0.25x + 6.00 represents the cost y of mailing a letter to Vienna, Austria based on the weight x of the letter in ounces. The flat rate of $6.00 is represented by the constant term 6.00 in the equation, and the additional charge of $0.25 per ounce is represented by the coefficient of x, which is 0.25.

To use this equation to determine the cost of mailing a specific letter, you would need to know the weight of the letter in ounces. You could then substitute this value for x in the equation and solve for y, which would give you the cost of postage in dollars.

For example, if a letter weighs 2.5 ounces, you could plug in x = 2.5 into the equation:

y = 0.25(2.5) + 6.00

y = 0.625 + 6.00

y = 6.625

So the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

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Answer:

I don't know if this helps.

Answer:150 times

Step-by-step explanation:

The average professional basketball player's salary is 6x10^6 dollars yearly, while the average American worker's salary is 4x10^4 dollars yearly.

To find how many times greater the average professional basketball player's salary is, we can divide the basketball player's salary by the worker's salary:

6x10^6 / 4x10^4 = (6/4)x10^(6-4) = 1.5x10^2 = 150

Therefore, the average professional basketball player's salary is 150 times greater than the average American worker's salary.

Answer: 7 years old

Step-by-step explanation: The two quickest ways to solve these types of problems are by guess and check, and systems of equations. I will show you how to solve this problem with systems of equations since it is a systematic method.

We can replace the ages of Ethan and David with variables. Ethan's age is x and David's is y. Ethan is 3 years older than David and this can be represented by: y+3=x since 3 will have to be added to David's age, y to get Ethan's age, x. A second equation we can make is x+y=17 since the sum of their two ages is 17. Now we solve the system by first isolating a variable and then plugging that into the second equation.

y+3=x         x is already isolated for us

x+y=17

(y+3)+y=17 We substitute x in the second equation for y+3

2y+3=17     Rearrange variables

2y=14

y=7             David's age, y, is 7.

Hope this helps!

Answer:

Jennifer went grocery shopping; She purchased supplies to make sandwiches.

Step-by-step explanation:

Out of all the other sentences, "Jennifer went grocery shopping; She purchased supplies to make sandwiches." is the only grammatically correct answer.