1/8 times y = 4 what is y

The roast needs to sit 116 minutes before it is ready to be eaten.

Let T(t) = temperature after t minutes

By Newton's Law of Cooling, T(t) = 75 + (185-75)e^kt = 75 + 110e^kt

Newton's law of cooling states that the rate of change of temperature of an object is directly proportional to the difference in temperature between the object and its surroundings. Mathematically, it can be expressed as:

dT/dt = k(T - T0)

Where:

dT/dt is the rate of change of temperature (in degrees per time unit, such as degrees per second)

k is the cooling constant (in units of 1/time), which is a measure of how quickly an object cools down and depends on the properties of the object and its surroundings

T is the current temperature of the object (in degrees)

(a). T(30) = 75 + 110e^30k = 150

⇒110e^30k = 75

⇒e^30k = 0.681818

⇒30k = ln(0.681818)

⇒k = -0.0127664

We know, T(t) = 75 + 110e^-0.0127664t

  So, T(45) = 75 + 110e^-0.0127664(45) ≈ 137°

(b).  T(t) = 100 when 75 + 110e^-0.0127664t = 100

⇒ e^-0.0127664t = 0.2272727

⇒-0.0127664t = ln(0.2272727)

 ⇒t ≈ 116 minutes

Therefore, The roast needs to sit 116 minutes before it is ready to be eaten.

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Answer:

To find the distance of the car from the foot of the building, you can use the tangent function and the information given:

distance = 24m / tan(40°)

The distance of the car from the foot of the building is approximately 27.4m

Step-by-step explanation:

The right answer involves doing both studies with the identical data set, drawing conclusions regarding means, and using a two-sided significance test.

An algorithm which it sets two ratios to the same value is called a fraction. You might, for instance, write its ratio as follows: 1: 3 in the case of 1 male & Three girls (for every one boy there are 3 girls) There are 3 out of 4 females and 1 out of 4 guys. 0,25 are men (by dividing 1 by 4)

A ratio that connects a part to yet another is a percentage. For instance, there are 100 students in the class containing 20 men or 80 women. The percentage of males is 20/100, or 20%. 80 out of 100, or 80%, are women.

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The degrees of freedom for the regression sum of squares in a regression model is determined by the number of variables that are being used to make predictions. For example, if you have three independent variables in your model, the degrees of freedom for the regression sum of squares would be 3.

The degrees of freedom for the error sum of squares is the total number of observations in your dataset, minus the number of independent variables used in the model.

The total sum of squares is the sum of the squared differences between each observation and the overall mean of the variable being predicted. This has the same number of degree of freedom as the error sum of squares, which is total number of observations -1.

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Answer:

[tex]\frac{19}{13}[/tex]

Step-by-step explanation:

expressing 9.5 ÷ 6.5 as a fraction , that is

[tex]\frac{9.5}{6.5}[/tex] ( multiply numerator and denominator by 2 for whole numbers )

= [tex]\frac{9.5(2)}{6.5(2)\\}[/tex]

= [tex]\frac{19}{13}[/tex] ← in simplest form

a fraction is in simplest form when no other value but 1 will divide into the numerator and denominator.

Answer:

  095

Step-by-step explanation:

You want the bearing from C to D, given that the bearing from D to C is 85° west of north.

The bearing from C to D will be the opposite of the bearing from D to C.

Bearing is measured clockwise from north, so the bearing shown from D to C is -85°. Its opposite is found by adding 180°.

  180° +(-85°) = 95°

The 3-digit bearing of D from C is 095.

The radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60. Therefore,  It move to 84 cm.

Circumference Of Circle:

The total length of the circle boundary. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park or a circular table needs this measure of circumference. The circumference is a length value and its units are the same as the length units. A circle is a round closed figure with all endpoints equidistant from a fixed point called the center.

The formula for the circumference of a circle is expressed using the values ​​of the circle's radius 'r' and 'pi'. It is represented by the equation of circumference = 2πr. Using this perimeter formula, if you don't have a value for the radius, you can use the diameter to find it. To calculate the circumference is to use the formula circumference = π × diameter.

If you need to calculate the radius or diameter, consider the circumference of a circle and use the following formula:

                    Radius = circumference/2π

Now,

According to the Question:

If the radius is 80cm

and,  the circumference is 2×π×80cm.

If the wheel rotates by 60° then a fraction 60/360 (= 1/6) of the circumference moves over the ground.  

Therefore, the distance moved is

                     [tex]\frac{2*\pi*80 }{6}[/tex]

               = 83.77580

               ≈ 84 cm.

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The simplest ratio between 5 gallons and 6 quarts is 10:3.

To convert 5 gallons to quarts, we can use the conversion factor that 1 gallon is equal to 4 quarts.

Therefore, 5 gallons is equal to 5 x 4 = 20 quarts.

Now we need to express this ratio in its simplest form.

To simplify the ratio, we can divide both the number of quarts and the number of gallons by their greatest common divisor (GCD).

The GCD of 20 and 6 is 2. So, dividing both numbers by 2, we get:

20 ÷ 2 = 10

6 ÷ 2 = 3

Therefore, the simplest ratio between 5 gallons and 6 quarts is 10:3.

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On solving the provided question, we can say that the, probability P( 24 period hour) = 5/24

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

here,

E1 = stops at 5 clock

E2 = start at 24 hours

P( 24 period hour) = 5/24

the, probability P( 24 period hour) = 5/24

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The sales commission the clerk will receive if she sells the ring at a markdown of 10% is $61.87.

Sales commission is a percentage of the sales price paid to salespeople as an incentive to drive more sales for the organization.

The markdown price is the reduced selling price of an item.

It is determined by subtracting a stated percentage from the regular retail price.

Retail prices may be marked down to encourage customers' patronage during low sales periods.

The normal selling price of the ring = $549.99

Special promotion markdown = 10%

Marked-down price = $494.99 ($549.99 x 1 - 10%)

Sales commission in percentage = 12.5%

Sales commission in dollars = $61.87 ($494.99 x 12.5%)

Thus, the sales clerk will receive $61.87 in sales commission for selling the ring.

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The classroom should have 28-42 pots.

To find the number of pots needed for a classroom, you first need to determine the total floor space in square feet. If the classroom has a length of 35 feet and a width of 40 feet, the total floor surface area is 35 feet * 40 feet = 1400 sq ft.

The scientist suggests providing two or three pots of flowers for every 100 sq ft of floor space. To find the number of pots needed for 1400 sq ft of floor space, you can divide 1400 sq ft by 100 sq ft/pot.

So 1400 sq ft / 100 sq ft/pot = 14 pots

The researcher suggests a minimum of 2 pots per 100 sq ft of floor space, therefore, the classroom needs at least 2 pots. The researcher also suggested a maximum of 3 pots per 100 sq ft of floor space,

Therefore, the classroom should have between 2 and 3 pots of flowers per 100 sq ft of floor space, which means that the classroom should have between 28 and 42 pots of flowers.

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add the two sides together, giving us 8.4v + 13.4, which is the perimeter of the rectangle in centimeters.

2(4.2v - 2.6) + 2(1.5v + 6.7) = 8.4v + 13.4

1. Multiply the width by two to get the two sides: 2(4.2v - 2.6)

2. Multiply the length by two to get the other two sides: 2(1.5v + 6.7)

3. Add the two sides together to get the perimeter: 8.4v + 13.4

To calculate the perimeter of the rectangle, we must first find the length of the two sides. To do this, we multiply the width by two, giving us 2(4.2v - 2.6). This gives us the length of the two sides opposite each other. We then multiply the length by two, giving us 2(1.5v + 6.7). This gives us the length of the other two sides. We then add the two sides together, giving us 8.4v + 13.4, which is the perimeter of the rectangle in centimeters.

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The binding constraints for the ideal response in a linear programming issue are

5X + 3Y < 30

2X + 5Y < 20

The term "linear programming" (LP), sometimes known as "linear optimization," refers to a technique for determining the optimal result in a mathematical model whose criteria are represented by linear relationships, such as the largest profit or lowest cost.

A specific type of mathematical programming is linear programming (also known as mathematical optimization).

Formally speaking, linear programming is a method for optimizing a linear objective function under the restrictions of linear equality and linear inequality.

Convex polytopes, a set defined as the intersection of a finite number of half spaces, each of which is determined by a linear inequality, make up its viable region.

A real-valued affine (linear) function defined on this polyhedron serves as its goal function.

An algorithm for linear programming determines where on the polytope this function occurs.

Hence, The binding constraints for the ideal response in a linear programming issue are

5X + 3Y < 30

2X + 5Y < 20

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2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.

4) The solution to the system of equations v(x) = b(x) is given as follows:

A. (-3.43, 6.30).

The standard definition of a cube function is given as follows:

y = ax³ + bx² + cx + d.

As all the coefficients are positive, the definition is this one.

The system of equations for this problem is defined as follows:

The solution for the system of equations in this problem is approximated graphically.

The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.

From the graph given at the end of the answer, the coordinates of the point of intersection are given as follows:

(-3.432, 6.296).

Meaning that the solution to the system of equations is approximated by option A.

Item 2 asks for the standard cube function, with positive coefficients.

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The longest side of the given triangle can be calculated by using the cosine rule: b² = a² + c² - 2(ca)(cos B) where 'b' represents the longest side of the triangle opposite to largest angle B.

As given in the question,

Let us consider a triangle ABC,

Side opposite to ∠A = a

Side opposite to ∠B = b

Side opposite to ∠C = c

Let angle B be the largest angle then 'b' is the longest side.

To calculate the measure of the longest side using given measure apply :cosine rule :

b² = a² + c² - 2(ca)(cos B)

Therefore, to get the measure of the longest of a triangle apply cosine rule : b² = a² + c² - 2(ca)(cos B) where 'b' represents the longest side.

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Answer: 226

Step-by-step explanation:

Substitute -8 into x. You will get,

4 (-8)² + 4(-8) + 2

4 x 64 - 32 + 2

256 - 30

226

Answer: 226

Step-by-step explanation:

So the question's asking you to solve for f(-8) which basically means to substitute the x in the equation of f(x) with -8 and solve.

It will then look like this:

f(-8)= 4(-8)^2+4(-8)+2

Then just put it in a calculator and solve.

The value here is always 1, and the value should be 0, since it is a positive value for x.

About logarithmic base

A function whose logarithm is the base a of x. The exponential form is used here because it shows the inverse of the exponential function.

So we can conclude that positive values ​​of x here should always have values ​​1 and 0. So the above answer is correct.

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Answer:

c>9

Step-by-step explanation:

To start off the problem, we don't normally like fractions when we deal with solving equations, so in order to get rid of it, we can multiply the entire problem by 3, to get the inequality of 2c+3>21 which looks a LOT simpler to solve!

From here, we can minus 3 from both sides to get the problem 2c>18. After this, we can divide both sides by 2 to get c>9!

(One side note that might help you out in the future is that if you ever need to multiply or divide both sides by a negative number, the inequality sign switches, for example if it was originally a < sign then it now turns into a > sign)

The events A and B are mutually exclusive, that is they are independent. Hence, option a and option c are correct.

In probability theory, if two events don't happen at the same time, they are mutually exclusive or disjoint. The outcomes of a single coin flip, which can result in either heads or tails but not both, are an obvious example.

Given that A and B are mutually exclusive events.

For mutually exclusive events the probability of event A occurring or event B occurring is summation of the probability of the individual event.

Both the events are independent.

Hence, option a and option c are independent.

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Answer: h= 4/5yr+ 5

Step-by-step explanation: by looking at the graph the slope is 4/5 and it intercepts the graph at 5 so y=4/5x + 5, then I plugged in the variables on the graph to get yr for year and h for height

Sally's temperature is 99.07°F if human body temperatures have a mean of 98. 20° F and a standard deviation of 0. 62° F and her temperature can be described by z = 1.4.

Therefore the answer is 99.07°F.

To get this answer, you need to know how to convert standard scores (z-scores) back into original units.

As z = (x - μ)/ σ

Formula to convert z-score to original units is:

x = μ + (z × σ)

where x is the original value, μ is the mean, z is the standard score, and σ is the standard deviation.

Plugging in the given values we get

x = 98.2 + (1.4 × 0.62)

x = 98.2 + 0.868

x = 99.068

which round off to 99.07°F

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In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.

Let a1 be the first term....then the successive terms are

3a1 + 4,  9a1 + 16,  27a1 + 52,  81a1 + 160    

So  81a1 + 160 = 403     subtract 160 from each side

81a1 = 243    divide both sides by 81

a1 = 3

in other word

403 - 4 = 399/3 = 133

133 - 4 = 129/3 = 43

43 - 4 = 39/3 = 13

13 - 4 = 9/3 = 3

So, first term = 3

In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.

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Length of AB = c = 7.12

Measures of angles:

A = 56°

B = 34°

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AB² = AC² + BC²

Given in the figure,

AC = 3.96

BC = 5.96

AB = ?

A = ?

B = ?

By Pythagoras theorem

AB² = AC² + BC²

AB² = 3.96² + 5.96²

AB² = 15.6816 + 35.5216

AB² = 51.2032

AB = √51.2032

AB = 7.1156

Rounded to nearest hundredth

AB = 7.12

Now, tan B = AC/BC

tan B = 3.96/5.96

tan B = 0.6644

B = tan⁻¹ (0.6644)

B = 33.6°

Sum of Interior angles of a triangle = 180°

A + B + C = 180°

A + 33.6° + 90° = 180°

A + 123.6° = 180°

A = 180° - 123.6°

A = 56.4°

Rounded to nearest degree,

A = 56°

B = 34°

Hence,  7.12 is the measure of AB, 56° and 34° are the measures of angles A and B respectively.

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Answer:

Step-by-step explanation:

187

153

197

207

Different types of units are CGS system units, FPS system units, MKS system units and SI units.

The (CGS)centimetre-gram-second system of units is how this is expressed. The metric system employs the centimetre to represent length or distance, the gram as the fundamental unit to represent mass or weight, and the second to represent time. Although there are other units of measurement in the system, they are all derived from just a few of these.

The (FPS)foot-pound-second system of units is what this is in its entire form. In this metric system, the foot serves as the default unit of length, and the pound serves as the default unit of mass and force. Finally, time is represented by the second.

This system's full name is (MKS)meter, kilogram, and second. The measuring of physical quantities is indicated by the usage of this metric system. Here, a meter is used to indicate length and a kilogram to indicate mass. Prior to their redefinition, it was renowned for establishing the foundation for the SI units.

International System of Units(SI) is the lengthier abbreviation for the units. It is the most recent and contemporary variety of metric system in use today. It is frequently utilized as the reference unit of measurement. It primarily includes the following seven units of measurement: second, metre, kilogram, ampere, Kelvin, Mole and candela.

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The total surface area of the remaining solid is 443.14cm2

A three-dimensional object's surface area is the sum of all of its faces. Real- world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.

Here,

Given:

h = 15, r = 8cm

Slant height of cone

1 = r2+h2 = (8)2 + (15)2 = 17

Total Surface Area = Curved Surface area of Cylinder + Curved Surface area of Conical Part + Area of Circular

=2arh+arl+πr2

=2(3.14)(8) (1.5) + (3.14) (8) (17) + (3.14)(17)2 =443.14cm2

Therefore , the solution of the given problem of surface area comes out to be 443.14cm2.

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Multiplying the sample size by 4 reduces the standard deviation to half of the previous value, so a sample size of 30(4) = 120 would reduce the standard deviation of the sampling distribution to one-half of the value found in 35(b).

Now, According to the question:

Let's Know:

What is Standard Deviation?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Multiplying the sample size by 4 reduces the standard deviation to half of the previous value, so a sample size of 30(4) = 120 would reduce the standard deviation of the sampling distribution to one-half of the value found in 35(b).

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The loop is 4112.16 kilometers long.

To solve this problem, we can set up the following equation:

distance = speed x time

We know that Sarah's current speed is s km/hr, and that the loop is d kilometers long. We also know that her current time is 2 hours and 40 minutes, or 160 minutes.

From the information given, we know that if Sarah increases her speed by 1 km/hr, her time around the loop would be reduced by 6 minutes. Therefore, we can set up the following equation:

d = (s + 1)(160 - 6) = (s + 1)154

We also know that Sarah's current speed is s km/hr, and that the loop is d kilometers long and the time she takes is 160 minutes. Therefore, we can set up the following equation:

d = s * 160

We can now solve for s by substituting the first equation into the second equation:

d = s * 160

d = (s+1)154

s160 = (s+1)*154

We can now solve for s

s = 154/6 = 25.66 km/hr

Now we can plug in s into the first equation we have:

d = s * 160

d = 25.66 * 160

d = 4112.16 km

The loop is 4112.16 kilometers long.

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