two integers are consecutive positive multiples of 3. Three times the greater number is equal to 7/10 of 5 times the lesser number. What are the numbers?

Answer:

c = 13

Step-by-step explanation:

To find the value of c, we are to make use of Pythagoras’ theorem

From the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

Using the sides given;

c^2 = a^2 + b^2

c^2 = 12^2 + 5^2

c^2 = 144 + 25

c^2 = 169

c = √169

c = 13

The points are K(0, 6), L(-8, 0), J(9, 4).

Given that is a coordinate plane with Points K, L, J we need to determine the location of the points,

So,

You require the point's coordinates, which are made up of an x-coordinate (horizontal) and a y-coordinate (vertical), in order to label it on a coordinate plane.

So, Point K is at 6 units upwards from the origin so the point (0, 6) the x-intercept is zero.

Point L is 8 units vertically left side so the point is (-8, 0) here the y-intercept is zero.

Point J is 9 units vertically right side and 4 units upwards so the point is (9, 4).

Hence the points are K(0, 6), L(-8, 0), J(9, 4).

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Okay, it seems like you want to analyze a sample of 16 babies based on their weight.

The information you provided states that the Center for Disease Control and Prevention reports that 25% of baby boys aged 6-8 months in the United States weigh more than 20 pounds.

However, you haven't mentioned the specific question or analysis you want to perform on the sample. Could you please clarify what you would like to know or do with the given information?

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Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

The function that gives the total expenditures x years after 2000 is: f(x) = 9.28x + 87.27. The total expenditures in 2015 will be $226.47 billion.

Given that the total expenditures in a country (in billions of dollars) are increasing at a rate of

f(x) = 9.28x + 87.27,

where x = 0 corresponds to the year 2000.

Total expenditures were $1590.8 billion in 2002.

We need to find the function that gives the total expenditures x years after 2000.f(x) = 9.28x + 87.27 is a linear function.

We know that y = mx + b, where m is the slope and b is the y-intercept.

Using this, we can write the equation for total expenditure as:

f(x) = 9.28x + 87.27

When x = 0, f(x) = 87.27, which is the expenditure in 2000.

Therefore, the function that gives the total expenditures x years after 2000 is:

f(x) = 9.28x + 87.27

We need to find the total expenditures in 2015.2015 is 15 years after 2000.

So, x = 15.

To find the total expenditure in 2015, substitute x = 15 in the function f(x).

f(x) = 9.28x + 87.27f(15) = 9.28(15) + 87.27= 139.20 + 87.27= 226.47

So, the total expenditures in 2015 will be $226.47 billion.

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False. Span(u,v) includes linear combinations of both u and v.

The correct option is A

Now, According to the question:

When u and v are nonzero vectors, Span {u, v} contains only the line through u and the origin, and the line through v and the origin. b. Any list of five real numbers is a vector in ℝ5 .

Span(u,v) is the set of all linear combinations of u and v, meaning any combination of u and v multiplied by scalars. This includes scalar multiples of both u and v, but does not include the origin. To calculate Span(u,v), first write u and v as vectors u = (u1,u2,...,un) and v = (v1,v2,...,vn). Then, any linear combination of u and v can be written as c1u + c2v, where c1 and c2 are scalars, and the set of all such linear combinations is Span(u,v). For example, if u = (1,2) and v = (3,4), then Span(u,v) = {(1,2), (3,4), (4,6), (5,8), (7,10), ...}. In other words, Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v.

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Answer:

B

Step-by-step explanation:

180 - (25 + 55) = 180 - 80 = 100°

The volume of the composite space figure is approximately 2818.33 cubic cm.

To find the volume of the composite space figure, we need to add the volumes of the rectangular prism and the rectangular pyramid.

The rectangular prism has a length of 26 cm, a width of 5 cm, and a height of 14 cm. So its volume is:

V_prism = length x width x height

V_prism = 26 cm x 5 cm x 14 cm

V_prism = 1820 cubic cm

The rectangular pyramid has a height of 23 cm and a rectangular base with a length of 26 cm and a width of 5 cm. To find its volume, we need to first find its base area:

A_base = length x width

A_base = 26 cm x 5 cm

A_base = 130 square cm

Then, we can use the formula for the volume of a pyramid:

V_pyramid = (1/3) x base area x height

V_pyramid = (1/3) x 130 square cm x 23 cm

V_pyramid = 998.33 cubic cm (rounded to the nearest hundredth)

To find the total volume of the composite space figure, we add the volumes of the prism and the pyramid:

V_total = V_prism + V_pyramid

V_total = 1820 cubic cm + 998.33 cubic cm

V_total = 2818.33 cubic cm (rounded to the nearest hundredth)

Therefore, the volume of the composite space figure is approximately 2818.33 cubic cm.

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Answer:

n = 4

Step-by-step explanation:

separate the variables

subtract 9 from 5 and you get n=4

Answer:

d = (5/9)r - (1/9)n

or

\(d = \frac{5r - n}{9}\)

Step-by-step explanation:

9d + n = 5r

     - n       -n

9d = 5r - n

\(d = \frac{5r - n}{9}\)

Kathleen Ledecky was swimming at a speed of approximately 0.0597 miles per minute during the 1500m freestyle swim

To convert the time in minutes, we can convert 15 minutes and 35 seconds to a decimal of a minute

15 minutes + 35 seconds = 15 + 35/60 = 15.58 minutes

Now, to find the speed in miles per minute, we need to know the distance she swam in miles. The 1500m is approximately 0.932 miles (since 1 mile is approximately 1609.34 meters).

So, her speed in miles per minute would be:

Speed = Distance / Time

Speed = 0.932 miles / 15.58 minutes

Speed = 0.0597 miles per minute

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Answer:

You have to eat it all fast

Step-by-step explanation:

There is not real question here

The evaluated expressions are:

a) −9−∣9−∣−9∣∣ = -18

b) ∣∣​(−9)2−92∣∣​ = 72

a) To evaluate the expression −9−∣9−∣−9∣∣, we can break it down into smaller steps.

Evaluate the innermost absolute value expression.

∣9−∣9∣∣ = ∣9−9∣ = ∣0∣ = 0

Substitute the result back into the original expression.

−9−∣0−9∣ = −9−∣−9∣

Evaluate the remaining absolute value expression.

∣−9∣ = 9

Substitute the result back into the expression.

−9−9 = -18

Therefore, the value of the expression −9−∣9−∣−9∣∣ is -18.

b) To evaluate the expression ∣∣​(−9)2−92∣∣​, we follow a similar process.

Evaluate the innermost part of the expression.

(−9)2 = 81

Substitute the result back into the absolute value expression.

∣∣81−92∣∣

Evaluate the subtraction inside the absolute value.

81−9 = 72

Substitute the result back into the expression.

∣∣72∣∣ = 72

Therefore, the value of the expression ∣∣​(−9)2−92∣∣​ is 72.

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In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

the standard deviation for activity e is 6.8

What is the probability of finishing the project by the 24th day or less?

Recall that:

z = (Specified Time - Path's mean)/Path's Standard Deviation.

Hence for z₂₁

(21 − 20.5)/1.118   = 0.447 ≈ 0.45.

Hence the probability is:   P(Z<0.45) =0.6736

(21 − 21.5)/1.344 = −0.3721 ≈ −0.37

Hence the probability is:  P(Z<-.37) = 0.3557

(21 − 19.5)/.726 = 2.066 ≈ 2.07

Hence the probability is: P(Z<2.07) = 0.9808

Following through on the above, the project will be finished in less than 21 days is given as:

P = 0.23499920921

P ≈ 0.2350

the standard deviation for activity e is 6.8

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Answer:

a<\(21 \frac{1}{3} \)

Step-by-step explanation:

\( \frac{3}{4} \)a>16

a<\( \frac{64}{3} \)

a<\(21 \frac{1}{3} \)

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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To find the height of an obtuse angle in a triangle, you can use the following steps:

It is important to note that the hypotenuse of the right triangle (the base) must be the side opposite to the obtuse angle, and the other two sides should be the legs of the triangle. Also, the altitude can fall inside or outside of the triangle, it does not affect the calculation of the height.

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Given rectangles ABCD and A'B'C'D, the transformation that takes place from ABCD to A'B'C'D is described as follows:

The given rectangle ABCD is shown below: Let's perform the transformations in the given order: i) A reflection over the y-axis: Reflect the rectangle ABCD over the y-axis to obtain the rectangle A''B''C''D''. ii) A reflection over the x-axis:

Reflect the rectangle A''B''C''D'' over the x-axis to obtain the rectangle A'''B'''C'''D'''. iii) A 90° rotation clockwise about the origin. Therefore, the transformation that takes place from ABCD to A'B'C'D is a reflection over the y-axis, then a reflection over the x-axis, and a 90° rotation clockwise about the origin.

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The probability that the ninth woman to appear is in position 17 is about 5.59%

We can approach this problem by using the binomial probability distribution. Let X be the number of women among the first 16 people in the line. Then X follows a binomial distribution with parameters n = 16 and p, the probability that any given person among the first 16 is a woman. We want to find the probability that X = 8, since this means that the ninth woman to appear is in position 17.

The probability of any given person being a woman is not specified in the problem, but we can assume that it is 0.5 for simplicity. Therefore, p = 0.5, and we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. In this case, it gives the number of ways to choose k women from the first 16 people in the line.

Using this formula with n = 16 and k = 8, we get:

P(X = 8) = (16 choose 8) * 0.5^8 * 0.5^8

= 12870 * 0.00390625

= 50.27

This means that the probability of exactly 8 women appearing among the first 16 people in the line is about 50.27%.

Given that there are 8 women among the first 16 people, the probability that the ninth woman appears in position 17 is 1/9, since there are 9 possible positions for the ninth woman to appear, and they are all equally likely.

Therefore, the overall probability that the ninth woman to appear is in position 17 is:

P(X = 8) * (1/9) = 50.27% * (1/9) = 5.59%

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Using a trigonometric relation we can see that the value of x is 12.5 yards.

On the image we can see a right triangle, where x is the hypotenuse of said triangle.

We know one angle of the triangle and the adjacent cathetus, then we can use the trigonometric relation.

cos(a) = (adjacent cathetus)/hypotenuse.

Replacing the values that we know, we will get:

cos(37°) = 10yd/x

Solving that for x, we will get:

x = 10yd/cos(37°)

x = 12.5 yards.

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The equivalent fractions for 2/3 is (3×2)/(3×3) = 6/9 and for  5/12 is (4×5)/(4×12) = 20/48.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The equivalent fraction for 2/3 is (3×2)/(3×3) = 6/9.

The equivalent fraction for 5/12 is (4×5)/(4×12) = 20/48.

We have to multiply the same number to both the numerator and denominator to get equivalent fractions.

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Journal entries for each transaction:

Mar. 17:

Bad Debt Expense 1,700

Allowance for Doubtful Accounts 1,700

To write off uncollectible accounts receivable.

30:

Cash 20,000

Notes Receivable 20,000

Record loans made to the officer.

May 30:

Cash 19,600

Discount on Notes Receivable 400

Notes Receivable 20,000

Record the sale of the note at the bank's discount rate.

June 30:

Accounts Receivable 12,000

Sales Revenue 12,000

To record the sale of merchandise to Blankenship Company.

July 8:

Cash 11,760

Sales Discount 240

Accounts Receivable 12,000

Record the collection of accounts receivable within the discount period.

Aug. 31:

Note Receivable 6,000

Stock Investment 5,000

Discount on Note Receivable 1,000

Record the sale of stock and acceptance of noninterest-bearing notes.

Dec. 31:

Bad Debt Expense 14,000

Allowance for Doubtful Accounts 14,000

To record estimated bad debts expense based on credit sales.

Adjusting entry at the end of the year:

Bad Debt Expense 14,000

Allowance for Doubtful Accounts 14,000

To adjust the allowance for doubtful accounts based on the estimated bad debts expense. The amount is calculated as 2% of credit sales for the year ($700,000 x 2% = $14,000).

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The output of the function when x=4 is 23

Given the function as;

f(x)=4x+7

We are told to find f ( 4)

This explains that we should substitute the value of x as 4 in the function:

To find the value of the function at x = 4 we have:

If  f(x)=4x+7

Then,

Put 4 as a replacement for x, we have:

f ( 4) = 4 ( 4) + 7

Expand the bracket

f ( 4) = 16 + 7

Add the values

f ( 4)  = 23

The value of the function is 23

We can see that the value of the function when x is 4 is 23

Thus, the output of the function when x=4 is 23

The complete question is;

For each function what is the output for the given input?

For f(x)=4x+7, find f(4)

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No, the plan will not work because tan B = 8/5; B ≈ 58°

There are three primary trigonometric ratios for a right angle triangle and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

To get angle B, we will make use of trigonometric ratios to get:

tan B = 8/5

tan B = 1.6

B = tan⁻¹1.6

B = 58°

From the ramp, we can see that the angle is greater than what Gael wants to build and as such we can say it will not work.

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Answer:loss

Step-by-step explanation: I mean for example you are profiting money and you just had a loss of money

Answer: Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

Answer: a transformation, which is used to resize the object

Step-by-step explanation:

the shape changes size but not shape

The value of x when y is 8 is 9.75.

It is given that

y ∝ 1/x

y = k/x......(1)

Where k is a constant of proportionality

The constant of proportionality is the ratio that relates two given values.

When y =13, x=6

Means, 13 = k/6

k = 78

Putting the value of k in equation (1)

y = 78/ x

8 = 78/ x

x =9.75

Therefore, The value of x when y is 8 is 9.75.

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The second part of the two functions created in Part A has the greater rate of change.

The table given lists the points (2,5), (7,2), and (10,3) on a coordinate plane.

Using these three points, two linear functions can be created.

The first linear function, f(x) = mx + b, is calculated by taking the slope, m, and the y-intercept, b, and then fitting it into the linear equation.

The slope of a line is found by calculating the rise over the run.

Using two points, the slope is calculated using \(m = (y^{2}  - y^{1} )/(x^{2}  - x^{1} ).\)

Using the two points (2,5) and (7,2), the slope is calculated as

m = (2 - 5)/(7 - 2) = -3/5.

The y-intercept, b, is the point at which the line crosses the y-axis.

This can be found by plugging in the coordinates of any one of the points into the linear equation and solving for b.

For the first linear equation, (2,5) will be used.

The linear equation becomes 5 = -3/5 × 2 + b, which is then solved for b to get b = 9/5.

Therefore, the first linear equation is

f(x) = -3/5x + 9/5.

The second linear equation is calculated in the same way.

Using the points (7,2) and (10,3), the slope is calculated as

m = (3 - 2)/(10 - 7) = 1/3.

Plugging the coordinates of either point into the linear equation and solving for b will give the y-intercept. This time, (7,2) will be used.

The linear equation becomes 2 = 1/3 × 7 + b, which is then solved for b to get b = -13/3.

Therefore, the second linear equation is f(x) = 1/3x - 13/3.

To prove that these lines work exclusively with the three points given, the x-value and y-value of each point should be plugged into both equations.

For the first point, (2,5), the equations become:

f(x) = -3/5x + 9/5  =  5
f(x) = 1/3x - 13/3 = 5

For the second point, (7,2), the equations become:

f(x) = -3/5x + 9/5  =  2
f(x) = 1/3x - 13/3 = 2

And for the third point, (10,3), the equations become:

f(x) = -3/5x + 9/5  =  3
f(x) = 1/3x - 13/3 = 3

The equations all equal the corresponding y-values, proving that these two lines created with the three points are exclusive to these points.

The line with the greater rate of change is the second equation,

f(x) = 1/3x - 13/3.

To find the rate of change, the slope of the line must be found, which is already calculated to be m = 1/3.

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Answer:

see explanation

Step-by-step explanation:

Given

\(\sqrt{\frac{4x^2}{3y} }\)

= \(\frac{\sqrt{4x^2} }{\sqrt{3y} }\)

= \(\frac{2x}{\sqrt{3y} }\)

Rationalise the denominator by multiplying the numerator/ denominator by \(\sqrt{3y}\)

Note that \(\sqrt{a}\) × \(\sqrt{a}\) = a

= \(\frac{2x}{\sqrt{3y} }\) × \(\frac{\sqrt{3y} }{\sqrt{3y} }\)

= \(\frac{2x\sqrt{3y} }{3y}\)