Unit 3B Test
PART 1
Need THESE ANSWERS ASAP

Answer: 3.8 minutes!

Step-by-step explanation:

The answer is 3.8 minutes. To solve for t, we need to set up an inequality where the calories burned in routine #1 is equal to or greater than the calories burned in routine #2. We can write this as 22 + 5.75t ≥ 8.5t. Then, we can subtract 8.5t from both sides to get 22 ≥ -2.75t. Finally, we can divide both sides by -2.75 to get t ≤ -8/2.75, which simplifies to t ≤ 3.8. Therefore, Jane needs to run for 3.8 minutes in Routine #1 in order to burn at least as many calories as Routine #2.

Answer:

Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

Step-by-step explanation:

In Routine #1, the total number of calories burned is:

C1(t) = 22 + 5.75t

The first term represents the calories burned while walking, and the second term represents the calories burned while running.

In Routine #2, the total number of calories burned is:

C2(t) = 8.5t

This represents the calories burned while running, as there is no walking in Routine #2.

We want to find the values of t for which C1(t) is greater than or equal to C2(t). So we can set up the following inequality:

C1(t) ≥ C2(t)

Substituting the expressions for C1(t) and C2(t), we get:

22 + 5.75t ≥ 8.5t

Simplifying the inequality, we get:

22 ≥ 2.75t

Dividing both sides by 2.75, we get:

t ≤ 8

So Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

The figure below illustrates constructing: A. a bisector of a segment.

In Mathematics, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By critically observing the construction illustrated in the image attached above, we can logically deduce that it represents the bisector of line segment AB.

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The  triangle is rotated 90° counterclockwise about the origin shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

we have to rotate 90° counterclockwise about the origin.

as, the rule for 90° counterclockwise about the origin is (x, y) becomes

(-y, x).

As, the coordinates after rotation are :

(-8, 3)---> (-3, -8)

(-2, 8)---> (-8, -2)

(-5, 7) -----> (-7, -5)

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3/5 = 0,6, it is 0.6 × 100 = 60%

Therefore, 3/5 is expressed as 60% in terms of percentage.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.

According to the Question:

To convert a fraction to a decimal, it's always best to look at the denominator first. If the denominator only has prime factors of 2 and 5, you can easily pick a number multiplied by the denominator and convert it to a denominator that is a power of 10, and the result is the final prime number. If you have prime factors other than 2 and 5, converting to decimal takes longer and can result in infinite but repeating decimals.

In this case, the denominator is 5, so you can easily convert to decimal by multiplying the denominator and numerator by 2.

(3 × 20) / (5 × 20) = 60/100

Now,

To convert a fraction to a percentage, simply multiply by 100 and put a % sign next to the result.

As 3/5 = 0,6, it is 0.6 × 100 = 60%

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The 4-2-1 rule is a guideline used to help determine the amount of water an individual needs to drink each day.

The rule states that an individual should drink 4 liters of water for every 50 pounds of body weight, 2 liters of water for every 50 pounds of body weight if they are exercising, and 1 liter of water for every 50 pounds of body weight if they are in a hot or dry environment.

To calculate how much water you need to drink using the 4-2-1 rule, simply follow these steps:

1. Determine your body weight in pounds.
2. Divide your body weight by 50 to get the number of 50-pound increments in your weight.
3. Multiply the number of 50-pound increments by 4 to get the amount of water you need to drink if you are not exercising or in a hot or dry environment.
4. Multiply the number of 50-pound increments by 2 to get the amount of water you need to drink if you are exercising.
5. Multiply the number of 50-pound increments by 1 to get the amount of water you need to drink if you are in a hot or dry environment.
6. Add the amounts from steps 3, 4, and 5 together to get the total amount of water you need to drink each day.

For example, if you weigh 150 pounds, you would need to drink 4 liters of water for every 50 pounds of body weight (150 / 50 = 3), 2 liters of water for every 50 pounds of body weight if you are exercising (3 x 2 = 6), and 1 liter of water for every 50 pounds of body weight if you are in a hot or dry environment (3 x 1 = 3). Therefore, you would need to drink a total of 13 liters of water each day (4 + 6 + 3 = 13).

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Answer:

4/7 to decimal rounded to nearest thousandth is 0.571

The amount of baking soda he used is 1.5 teaspoons.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given that

When 5 cups of flour are used in a recipe, 2.5 teaspoons of baking soda are required.

Anna wants to reduce the recipe to only 3 cups of flour.

We have to determine

How much baking powder should he use?

According to the question

Let x be the amount of baking soda he used,

A recipe for waffles calls for 5 cups of flour and 2.5 teaspoons of baking powder.

If Jason uses 3 cups of flour.

Then,

The amount of baking soda he used is

x/3 = 2.5/5

solving we get,

x = 1.5

Hence, The amount of baking soda he used is 1.5 teaspoons.

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The height of flagpole C is approximately 6.1 feet.

Distance is a numerical measurement of how far apart or how far away objects or locations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it only has magnitude and no direction.

The distance between two points is typically calculated using a formula, such as the distance formula in Euclidean geometry, which involves taking the square root of the sum of the squares of the differences in the coordinates of the two points.

Let's start by drawing a diagram of the situation:

          A

          |

          |

          |

          |

          |

          |

          |

-----------S-----------C

We can see that the triangles ASC and ABC are similar, since they have the same angles (90 degrees at S and a common angle at A). Therefore, we can use proportions to find the height of flagpole C:

AC   SC

-- = --

AB   AS

Substituting the given values, we get:

AC   10

-- = --

AB   AB + 12

We can solve for AB by noting that the height of flagpole A is the sum of the heights of AB and BC:

13.2 = AB + BC

Solving for BC, we get:

BC = 13.2 - AB

Substituting this into the first equation, we get:

AC   10

-- = --

AB   AB + 12

AC = 10(AB)/(AB + 12)

Now we can substitute the value we found for AB:

AC = 10(13.2 - BC)/(13.2 - BC + 12)

AC = 10(13.2 - BC)/25.2

We still need to find BC, which we can do by using the fact that the triangles ABC and ASC are similar:

BC/AB = SC/AS

Substituting the given values, we get:

BC/AB = 10/22

BC = 10AB/22

Substituting this into the equation for AC, we get:

AC = 10(13.2 - 10AB/22)/25.2

Now we can solve for AB:

13.2 = AB + 10AB/22

AB = 7.92

Finally, we can substitute this into the equation for AC:

AC = 10(13.2 - 10(7.92)/22)/25.2

AC = 6.1

Therefore, the height of flagpole C is approximately 6.1 feet.

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The length of the side AB in triangle ABC is 6.58 units.

What are trigonometric ratios in terms of a right-angle triangle?

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjacent/hypotenuse and

tan = opposite/adjacent.

From the given figure we can conclude that we have length of the adjacent

with an angle of 20° and we have been asked to find the hypotenuse.

We know cos = adjacent/hypotenuse.

∴ cos20° = adjacent/7.

0.937 = adjacent/7.

adjacent = 7*0.937.

adjacent = 6.58.

Hence , the length of the side AB in triangle ABC is 6.58 units.

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Answer:

the answer is y=/0.375x

Step-by-step explanation:

Answer:

y=1/3x+4

Step-by-step explanation:

Yep

A relation in math is a set of ordered pairs containing two elements, one from each set. The first element is from the domain and the second from the range.

Relations can be expressed as a set of ordered pairs, as a graph, or as a mapping diagram. A function is a special type of relation in which, for every element in the domain, there is one and only one element in the range. This is expressed mathematically by stating that for every x in the domain, there is one and only one y in the range such that y = f(x). To calculate a relation, the domain and range values are paired with each other, and the ordered pairs are written down. For example, if the domain is {2,3,4,5} and the range is {7,8,9,10}, then the relation would be {(2,7),(3,8),(4,9),(5,10)}.

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Answer:

0, 1, 2, or 3

Step-by-step explanation:

        0 + 7 = ≥ 10

        It is true.

        1 + 7 = ≥ 10

        It is true.

        2 + 7 = ≥ 10

        It is true.

        3 + 7 = ≥ 10

        It is true.

        4 + 7 = ≥ 10

        It is false.

Based on the information provided, it can be concluded that Licia's piece of wood is 10 1/8 long.

To determine Licia's piece of wood, let's first consider the information given:

Based on this, to find out the length of Licia's let's add the fractions provided, the process is shown as follows:

Licia piece of wood = 8 1/2 + 1 5/8= 17/2 +13/8= 81/8= 10 1/8

Therefore, Licia's piece of wood is 10 1/8

This result is equal to 10,125

1/8 = 0,125

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Answer:

300 w

Step-by-step explanation:

swim this question we have an equation w = 21 25 - 2012 I square which represents the power w where w is the power in watts and 120 volt circuit is there which has a resistance of 12 ohm when current I is flowing through the circuit the voltage resistance and current is what is the maximum power in war that can be delivered in this circuit so we have to find out the maximum value of power that can exist in the circuit with 120 volts AC circuit and 12 homes of resistance ok so to find the maximum value of this in an equation we need to find vi we can the best way is we can find out the Maxima Abhishek creation and how do you

find the maximum to find the maximum we can differentiate this equation with respect to I and when the equator when we will equip the differentiation of this equation 20 the value of I that will obtain that will be obtained after doing this will be the maximum for this equation let me show you how that is differentiate DW by D I can we differentiate this this equation with respect to I we get 120 - 24 I know what we have to do this week with this 20 now 120 - 24 I = 20 with this I = 25 we get the value of equal to 55 is the maximum for this equation which means that if we put the value of I

45 we replace if the Avengers equation replace iPhone 5 will get the maximum value of w which is what you wanted right we wanted the maximum power in watts letters replace I buy 5 this equation the equation is 120 I -12 I square be replaced by 5 we get the answer as 300 w this is our answer

The value of x is 9. A quadrilateral having four equal, right-angled angles is called a rectangle.

The following formula determines a rectangular prism's volume:

V = l × b × h

To achieve, we substitute the dimensions.

V = 6 × 3 × 12 in^3

The rectangular pyramid's volume is,

V = 1/3 × 6 × 12 × x in^3

Comparing the two volumes results in,

1/3 × 6 ×  12 × x = 6 × 3 × 12

We divide through by 6 × 12 to get,

x/3 = 3

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The value of the expression is -8. Option A

It is important to note that algebraic expressions are expressions that are made up of variables, terms, coefficients, constant and factors.

From the information given, we have that;

3x-6= 5x - 2

collect like terms

3x - 5x = -2 +6

subtract the like terms

-2x = 4

Make 'x' subject

x = -2

Substitute the value in the equation

2x - 4

2(-2) - 4

expand bracket

-8

Hence, the value is -8

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The values for x by completing the given steps to solve for |x/6 - 7/12| = 11/6 is x=29/2 or x= -15/2.

A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables.

Given is a modulus function, |x/6 - 7/12| = 11/6

Solving for x,

Negative Direction;

x/6 - 7/12 = -11/6

x/6 = -22/12 + 7/12 = - 15/12

x = (-15/12)6 = -15/2

x = -15/2

Positive Direction;

x/6 - 7/12 = 11/6

x/6 = 22/12 + 7/12 = 29/12

x = (29/12)6 = 29/2

x = 29/2

Hence, the values for x by completing the given steps to solve for |x/6 - 7/12| = 11/6 is x=29/2 or x= -15/2.

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The question is not complete the similar question is solved.

H0: mean=1.45

H1: mean< 1.45

=-3.175

The result is significant at p < .01.

Reject Null Hypothesis

the mean level of exhaust emitted for this model reduces emissions

A)

Null hypothesis:

H0: mean=1.45

Alternative hypothesis:

H1: mean< 1.45

b)

estimate - the value we hypothesize standard error test statıstıc - t-statisticS

[tex]\begin{gathered}\text { test statistic }=\frac{\text { estimate }-\text { value we hypothesize }}{\text { standard error }} \\\text { t-statistic }=\frac{\bar{x}-\mu_o}{s / \sqrt{n}}\end{gathered}[/tex]

t=1.21-1.45/0.4/sqrt(28)

=-3.175

c)

t=-3.175

df=28-1=27

alpha=0.01

The P-Value is .001863.

The result is significant at p < .01.

d)

p=0.001

< alpha of 0.01

Reject Null Hypothesis

e)

there is sufficient evidence

the mean level of exhaust emitted for this model reduces emissions

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Answer: You can make 5/3 * (1/1) = 5 servings with a cup of macaroni.

And, with 5 servings, you can make 5 * (3/1) = 15 1/3 servings of pasta salad.

Step-by-step explanation:

Answer:

<P = 41

Step-by-step explanation:

we can consider this first figure as a quadrilateral and the trianlgle attached to be is equilateral triangle (as it is already shown in the figure that sides are equal)

we know that each angle of equalateral triangle is 60°

we can see that angle 79° is attached to it and even other angle is also attached

let the other angle be x

we can notice that x and the angle of equi triangle make a linear pair

so 180 - 60

= 120°

the opposite angle to the angle x will be also equal as angles on the same side of qual sides will be equal

now we know that total angle sum of quadrilateral is 360°

so

79 + 120 + 120 + <P = 360

319 + <P = 360

<P = 360 - 319

<P = 41

The number of minutes that you walk directly from the parking lot to the house will be 12.73 minutes.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The house is located 1480 ft down a paved path that parallels the beach, which is 740 ft wide. Along the path, you can walk 330 ft/min, but on the beach, you can only walk 130 ft/min.

The distance between the house and the parking is given as,

d² = 740² + 1480²

d² = 547,600 + 2,190,400

d² = 2,738,000

d = 1,654.69 feet

Then the time taken is given as,

T = 1,654.69 / 130

T = 12.73 minutes

The number of minutes that you walk directly from the parking lot to the house will be 12.73 minutes.

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The standard deviation lies in the range of 0 to 1. The numerical value of standard deviation can never be negative.

The standard deviation is a measure of amount of variation or dispersion of a set of values. When we compare two unequal observations, the result is always greater than zero i.e., always positive.

Standard deviation is the square root of the variance of the observations and the root always gives values either positive or zero, it can never be negative.

Therefore, the numerical value of the standard deviation can be positive. The value of standard deviation is always greater or equal to zero.

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Answer:

Answer: x=12

6 x 12=72

Answer:

x = 12 .....................

Step-by-step explanation:

.

Answer: 3 + 3 adds up to 6, which is less than 10.

Step-by-step explanation:

Answer: 3

Step-by-step explanation: Someone is 15 steps behind in a race, then that is sectioned into a fifth. How many steps behind are they?

A medium-sized orange contains 68 calories. Which is one-fifth the number of calories in a slice of cheese pizza.

If one slice of cheese pizza contains 340 calories, and a medium-size orange has one-fifth that number of calories, we can find the number of calories in a medium-size orange by dividing 340 by 5. Calories in a medium-sized orange = [tex]\frac{340}{5}[/tex] calories = 68 calories. The division is an arithmetic operation used to find out how many times one number is contained within another number. The result of a division operation is called the quotient.

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The horizontal distance between Ryan and the dolphin is  57.87 feet.

The airplane is 10735.96 feet away from the control tower

The angle of depression from the top of the lighthouse to the boat is 0 degrees.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Using trigonometry, we can find the horizontal distance x:

tan(15) = x / 228

x = 228 tan(15)

x = 57.87 feet

Therefore, the horizontal distance between Ryan and the dolphin is  57.87 feet.

2. Using trigonometry, we can find the horizontal distance between the airplane and the control tower:

tan(56) = x / 7450

x = 7450tan(56)

x = 10735.96 feet

Therefore, the airplane is approximately 10735.96 feet away from the control tower

3. We want to find the angle of depression from the top of the lighthouse to the boat. Since the lighthouse is 275 feet above the water, we can use trigonometry to find the height of the lighthouse above the boat:

tan(90) = 275 / x

x = 275 / tan(90)

x = undefined

Therefore, the angle of depression from the top of the lighthouse to the boat is 0 degrees.

Hence,  the horizontal distance between Ryan and the dolphin is approximately 57.87 feet.

the airplane is approximately 10735.96 feet away from the control tower

the angle of depression from the top of the lighthouse to the boat is 0 degrees.

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Answer: 1181

Step-by-step explanation:

Answer:

10 packs

Step-by-step explanation:

Allie wants to give each of her classmates 3 pencils, so she needs a total of 3 pencils * 26 classmates = 78 pencils.

The pencils come in packs of 8, so she needs 78 pencils / 8 pencils per pack = 9.75 packs of pencils.

Since you can't buy a fraction of a pack, Allie needs to buy 10 packs of pencils.