Aaron is 5 years younger than
Roy. Four years later, Roy will be
twice as old as Aaron. Find their
present ages

Answer:

Step-by-step explanation:

I assume you are talking about square roots when you say root...

Sqrt(-9) = 3i

Sqrt(-12) = 2Sqrt(3)i

Complex number is 3 + 2Sqrt(3) i

Answer:

whole = 67.75

Step-by-step explanation:

Answer:

\(\sqrt{13}\)

Step-by-step explanation:

\(L^{2}\)=\(3^{2}\)+\(2^{2}\)=9+4=13

L=\(\sqrt{13}\)

Answer:

24 in by 28 in.

Step-by-step explanation:

In this scenario, one foot is two inches

Answer:

D prominent is spelled wrong that's how you spell it

Step-by-step explanation:

Answer:

the length of the shortest ladder is 11.41 feet

Step-by-step explanation:

The computation of the length of the shortest ladder is shown below:

AB^2 = AC^2 + BC^2

AB^2= (10)^2 + (5.5)^2

AB^2= 100 + 30.25

AB^2 = 130.25

AB = 11.41 feet

hence, the length of the shortest ladder is 11.41 feet

Answer:

See attached photo for work

Step-by-step explanation:



When dividing 210 by 3.5 using long division, the quotient is 60.

Dividing is a fundamental mathematical operation that involves splitting a quantity or set of items into equal parts. It is the inverse of multiplication, where one number, called the dividend, is separated into smaller portions or groups by another number, known as the divisor. The result is called the quotient. Division is denoted by the symbol "/", ÷, or ":".

When dividing 210 by 3.5 using long division, we start by dividing 2 by 3.5 which gives us 0 as the quotient. We then bring down the next digit, 1, and divide 21 by 3.5 which gives us 6 as the quotient. Finally, we bring down the last digit, 0, and divide 0 by 3.5 which gives us 0 as the quotient. Therefore, 210 divided by 3.5 is equal to 60.

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Answer:

Slope = \(-\frac{3}{4}\)

y-intercept = 2

Equation of the line 't': \(y=-\frac{3}{4}x+2\)

Step-by-step explanation:

Slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is represented by,

Slope 'm' = \(\frac{y_2-y_1}{x_2-x_1}\)

Since line 't' is passing through two points (0, 2) and (8, -4),

Slope of the line 't' = \(\frac{2+4}{0-8}\)

                           m = \(-\frac{6}{8}\)

                           m = \(-\frac{3}{4}\)

Since y-intercept of a line is the value of 'y' for x = 0 [from point (0, 2) lying on this line]

Therefore, Y-intercept of line 't' = 2

Slope intercept of an equation is,

y = mx + b

where m = slope of the line

b = y-intercept

Therefore, equation of the line 't' will be,

\(y=-\frac{3}{4}x+2\)

Answer:

C

Step-by-step explanation:

The result of the evaluation is 76,058.4 to the appropriate number of significant digits.

To evaluate the expression ((15)(18.3))/((0.0033)(11.27)), we simply perform the arithmetic operations following the order of operations (parentheses first, then multiplication and division from left to right).

(15)(18.3) = 274.5

(0.0033)(11.27) = 0.037191

Now, we divide 274.5 by 0.037191:

274.5 / 0.037191 = 7,364.56252...

Since we are asked for the appropriate number of significant digits, we round the result to the same number of significant digits as the least precise number in the original expression, which is 15 (2 significant digits).

Therefore, the final result, rounded to the appropriate number of significant digits, is 76,058.4.

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*see attachment for the diagram of the information given

Answer:

115.8°

Step-by-step explanation:

Due west = 83 miles

Northwest = 111 miles

Distance to its original position = 165 miles

Let x represent the degree north of west that it turned when it changed direction which is the opposite angle of 165 miles.

Thus, to find x, we'd apply the Law of Cosine which is given as:

c² = a² + b² - 2ab*cos C

Where,

C = x

a = 83 miles

b = 111 miles

c = 165 miles

Plug in the values

165² = 83² + 111² - 2*83*111*Cos x

27,225 = 19,210 - 18,426*Cos x

27,225 - 19,210 = - 18,426*Cos x

8,015 = -18,426*Cos x

8,015 = -18,426*Cos x

8,015/-18,426 = Cos x

-0.434983176 = Cos Cmx

Cos x = -0.434983176

x = cos^{-1}(-0.434983176)

x = 115.784223°

x = 115.8°

take the natural logarithm of both sides:

Divide both sides by ln(12):

Answer:

159.25 meters

Step-by-step explanation:

Using the solution diagram attached ;

From Trigonometric relation, the width, w of the canal can be obtained using :

Tanθ = opposite / Adjacent

Tan 37 = 120 / w

w * tan 37 = 120

w = 120 / tan 37

w = 159.24537 meters

Hence, width of canal is 159.25 meters

The quadratic expression cannot be factorized, because the discriminant is less than 0

The expression is given as:

x²+12x+180

Calculate the discriminant of the expresison using:

D = B² - 4AC

So, we have:

D = 12² - 4* 1 * 180

Evaluate

D = -576

Because the discriminant is less than 0, then the expression cannot be factorized

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Answer:

We have the problem:

|3r−15| if r<5

First we see the equality, if r = 5 we have:

I3r - 15I = I3*5 - 15I = I0I = 0.

Then the only restriction that we have is:

I3r - 15I > 0.

now, we could simplify it a bit further:

if r < 5, then the thing inside the absolute value will always be negative:

Then we can write:

I3*r - 15I = -(3*r -15) > 0

multiplying by -1 in both sides

(3r - 15) < 0.

if we keep simplifying this, we will get our initial restriction:

3r - 15 < 0

3r < 15

r < 15/3 = 5

r < 5

The radius of convergence is the distance from the center of a power series to the nearest point where the series converges, determined using the Ratio Test. The interval of convergence is the range of values for which the series converges, including any endpoints where it converges.

The radius of convergence of a power series is the distance from its center to the nearest point where the series converges.

To determine the radius of convergence, we can use the Ratio Test.

Step 1: Apply the Ratio Test by taking the limit as n approaches infinity of the absolute value of the ratio of consecutive terms.

Step 2: Simplify the expression and evaluate the limit.

Step 3: If the limit is less than 1, the series converges absolutely, and the radius of convergence is the reciprocal of the limit. If the limit is greater than 1, the series diverges. If the limit is equal to 1, further tests are required to determine convergence or divergence.

The interval of convergence can be found by testing the convergence of the series at the endpoints of the interval obtained from the Ratio Test. If the series converges at one or both endpoints, the interval of convergence includes those endpoints. If the series diverges at one or both endpoints, the interval of convergence does not include those endpoints.

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Answer: I think the answer is 81, but I don’t have a good explanation.

Step-by-step explanation: if you can find the angle next to 12x-3 (D), and the angle of 8+15x they should equal 180 degrees.

The Triangle Exterior Angle Postulate states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

In the given problem, the exterior angle is < JDC, and its measure is equal to the sum of the measures of < (12x -3)° and < 32°.

We can set up the following equality statement to solve for the value of x, and find out the measure of < JDC:

m < JDC° =  < (12x -3)° + < 32°

< (8 + 15x)° = < (12x -3)° + < 32°

Subtract 8 from both sides:

8 - 8 + 15x = 12x - 3 + 32 - 8

15x = 12x + 21

Subtract 12x from both sides:

15x - 12x = 12x - 12x + 21

3x = 21

Divide both sides by 3 to solve for x:

3x/3 = 21/3

x = 7

To verify whether the value for x is correct, substitute x = 7 into the equality statement:

m < JDC° =  < (12x -3)° + < 32°

< (8 + 15x)° = < (12x -3)° + < 32°

[8 + 15(7)]° = [12(7) - 3]° + 32°

8° + 105° = 81° + 32°

113° = 113° (True statement). Therefore, the correct value for x = 7.

Therefore, the correct answer is C) m < JDC = 113°.

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Everything has been explained in there

Answer:

3.5

Step-by-step explanation:

7/3= 3.5 or 3 1/2

The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

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The temperature at dawn is -7 F.

If it is  8 degrees colder at dawn than it is at dawn, it means that the temperature is lower in the dawn than it is in the dusk. Thus, to determine the temperature at dawn, subtract 8 from the temperature at dusk.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to represent subtraction is -.

Temperature at dawn = termpature at dusk - difference in termpature

1 - 8 = -7

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In the triangle ABC, i) ABC = 52.12° ii) BCA = 31.08° and iii) AB = 8.11cm.

Based on the provided information, ∠ BAC = 96.8°; AC = 12.4cm, and BC = 15.6cm

i) According to the law of sine,

Sin ∠A/a = Sin ∠B/b = Sin ∠C/c where a is the length opposite to ∠A, and so forth.

Hence, based on the information, ∠ABC = ∠B

Sin ∠B/AC = Sin ∠A/BC

Sin ∠B/12.4 = Sin 96.8/15.5

Sin ∠B = (Sin 96.8/15.5)*12.4

∠B = Sin^-1((Sin 96.8/15.5)*12.4)

∠B = 52.12°

ii) As the sum of interior angles of a triangle is 180°. ∠As BCA = ∠C

∠A + ∠B + ∠C = 180

96.8 + 52.12 + ∠C = 180

∠C = 31.08

iii) According to the law of cosine,

c^2 = a^2 + b^2 – 2ab cos C where C is the angle opposite to c.

BC^2 = AB^2 + AC^2 – 2(AB)(AC)cos98.6

15.6^2 = AB^2 + 12.4^2 – 2(AB)(12.4)cos98.6

Solving for AB,

AB = 8.11cm

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If r = 2 then substitute it for where r is in your given equation

New equation:

\(\dfrac{7(2)}{2}\)

\(\bf{7(2) = 14}\)

\(\dfrac{14}{2} = 7\)

\(\bf{Answer: 7}\) ☑️

Good luck on your assignment and enjoy your day!

\(\frak{LoveYourselfFirst:)}\)

The simplified equation is F(a, b, c, d) = ad.

In the original equation, F(a, b, c, d) is defined as the product of ab' and the expression (a'cd + (ad + b'c')')(a' + b). To simplify this expression using Boolean algebraic manipulation, we can apply various Boolean laws and identities.
Starting with the expression (a'cd + (ad + b'c')'), we can simplify it as a'cd + ad + b'c' using the distributive law. Next, we can simplify (a'cd + ad + b'c')'(a' + b) by applying the distributive law again, resulting in (a'cd + ad + b'c')(a') + (a'cd + ad + b'c')(b).
Simplifying further, we get a'acd + aad + a'b'c' + ab, which can be simplified to ad using the Boolean law aad = ad.
Therefore, the simplified equation is F(a, b, c, d) = ad.

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Answer: (6,7)

Step-by-step explanation:

Answer:

(7,6)

Step-by-step explanation:

look above as your axis x it's 7, and then down is axis y is 6.

Be aware that the other claims are untrue as 80 degrees is the angle B'OA and Triangles ABO and A'B'O are similar triangles are true .

A closed triangle is a two-dimensional plane shape with three angles and three straight sides. Three non-collinear points are connected with straight line segments to create one of the fundamental shapes in geometry. The lengths of the sides can vary depending on the type of triangle, but the sum of the interior angles of a triangle is always 180 degrees. Triangles with all three sides equal, such as equilateral triangles, isosceles triangles, and scalene triangles, are examples of frequent triangle types (where no sides are equal).

given

According to the diagram, the following claims are accurate:

80 degrees is the angle B'OA.

Triangles ABO and A'B'O are similar triangles.

Angle A'B'O and angle ABO are equivalent.

Line segment AB and line segment A'B' are congruent.

Be aware that the other claims are untrue as 80 degrees is the angle B'OA and Triangles ABO and A'B'O are similar triangles are true .

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Answer:

a. Kito has been billed correctly

Step-by-step explanation:

We simply need to check Kito's work to see if his price is accurate.

First, we can add the prices together to find the price before the sales tax is applied:  39.99 + 24.99 + 26.99 = $91.97

We can use this formula to figure out the total cost, C, after the sales tax, t is added:

C = l + (l * (t / 100)), where l = the price before applying the sales tax

C = 91.97 + (91.97 * (6 / 100)) = 97.4882 = $97.49

We know that the total cost lies between the 50 and 100 and that Kito chose the express shipping.  Thus we add:  97.49 + 8.20 = $105.69.

If we did not round before, we would still get the same answer when rounding:  97.4882 + 8.20 = 105.6882 = $105.69

Kito has not been charged enough for his purchase.

Option B is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we need to calculate the total cost of the purchase before shipping and taxes:

= $39.99 + $24.99 + $26.99

= $91.97

Next, we need to add the shipping cost based on the amount of the purchase:

Since the purchase amount is between $50 and $100, the express shipping cost is $8.20.

So the total cost of the purchase with shipping is:

= $91.97 + $8.20

= $100.17

Finally, we need to add the tax:

= 6% of $100.17

= $6.01

So the total amount Kito should be billed is:

= $100.17 + $6.01

= $106.18

And,

Since Kito was billed $105.69, he has been undercharged by $0.49.

Therefore,

Kito has not been charged enough for his purchase.

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The percentage of people with blood pressure between 115 and 165 mm is 68.27% (closest to option e). The percentage of people with blood pressure between 140 and 165 mm is 89.4% (closest to option b). The percentage of people with blood pressure over 165 mm is 10.6% (closest to option a).

To solve this problem, we can use the properties of the normal distribution, which is a continuous probability distribution that is often used to model real-world data. In particular, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages of people with blood pressure within certain ranges. The empirical rule states that, for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean. Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard  deviations of the mean. Using this rule, we can estimate the following  percentages: The percentage of people with blood pressure between 115 and 165 mm: First, we need to find the z-scores for the lower and upper limits of the range: z_lower = (115 - 140) / 20 = -1.25.

z_upper = (165 - 140) / 20 = 1.25

We can then use a standard normal distribution table or a calculator to find the areas under the curve corresponding to these z-scores:

P(-1.25 < Z < 1.25) = 0.7887 - 0.1056 = 0.6831

So, approximately 68.31% of people have blood pressure between 115 and 165 mm.

The percentage of people with blood pressure between 140 and 165 mm: In this case, the lower limit is equal to the mean, so we only need to find the z-score for the upper limit: z_upper = (165 - 140) / 20 = 1.25

Using the same approach as before, we get:

P(Z < 1.25) = 0.8944

So, approximately 89.44% of people have blood pressure between 140 and 165 mm. The percentage of people with blood pressure over 165 mm:

In this case, we only need to find the area to the right of the upper limit:

P(Z > 1.25) = 0.1056

So, approximately 10.56% of people have blood pressure over 165 mm.

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Complete Question

The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.

a. 10.6%

b. 89.4%

c. 39.4%

d. 78.8%

e. 68.27%

___ The percentage of people with blood pressure between 115 and 165 mm.

___ The percentage of people with blood pressure between 140 and 165 mm.

___ The percentage of people with blood pressure over 165 mm.

Answer:

between 7.0 and 9.0 hours of sleep

Step-by-step explanation:

got it right