Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?

What is the product of 2.31 and 0.21?

Solution:

We need to find 2.31*0.21

Let us first find 231*21, then we would consider decimals

231*1=231

231*2=462

So, 231*21=231+4620=4851

So, we get 231*21=4851

But, we need to find, 2.31*0.21

There are two numbers after decimal in 2.31 (3 and 1). and, there are two numbers after decimal in 0.21(2 and 1)

So, In result of, 2.31*0.21 there must be four digits after decimal.

As, 231*21=4851

So, 2.31*0.21=0.4851 (four digits after decimal)

Answer:0.4851

To solve this problem, we are going to use a proportion, letting the variable x represent the unknown number of cups of oatmeal that we need.

1.5 cups/36 cookies = x cups/60 cookies

To simplify a proportion like this, we can use cross-multiplication. This means multiplying the numerator of one fraction by the denominator of the other fraction and setting it equal to the product of the other numerator and denominator. This is modeled below:

(36)(x) = (1.5)(60)

To simplify, we begin by multiplying out each side.

36x = 90

Finally, we divide both sides of the equation by 36.

x = 2.5

This means that we need 2.5 cups of oatmeal to make the cookies.

Hope this helps!

Answer:

[tex](x,y)\rightarrow (-x,-y)[/tex]

Step-by-step explanation:

We are asked to find the the algebraic rule describes the 180° counterclockwise rotation about the origin .

We know that when we rotate a point 180° counterclockwise rotation about the origin , the x and y-coordinates change their sign.

[tex](x,y)\rightarrow (-x,-y)[/tex]

Therefore, our required rule is [tex](x,y)\rightarrow (-x,-y)[/tex].

Final answer:

The inequality representing the number of karate classes Theo can take is c ≤ 17, considering his budget after buying a dogi and the cost per class.

Explanation:

The question asks us to find the inequality that represents the number of karate classes, c, Theo can take given his budget scenario. Theo budgets $154 for his karate classes and spends $12 on a dogi. This leaves Theo with $154 - $12 = $142 for classes. Since each class costs $8, we divide the remaining budget by the cost per class to find the maximum number of classes he can take:

$142 ÷ $8 = 17.75.

Since Theo cannot attend a fraction of a class, we round down to 17. The inequality representing the number of classes Theo can take would be c ≤ 17, where c is the number of classes Theo can attend.

The inequality that represents the number of classes, [tex]\( c \)[/tex], that Theo can take is:

[tex]\[ 8c + 12 \leq 154 \][/tex]

To derive this inequality, we start by considering the total amount Theo has budgeted for karate classes, which is $154. From this budget, Theo has already spent $12 on purchasing a karate uniform. Therefore, the remaining amount available for attending the classes is [tex]\( 154 - 12 \)[/tex].

Now, each karate class costs $8, so the total cost for attending [tex]\( c \)[/tex] classes is [tex]\( 8c \)[/tex]. To ensure that Theo does not exceed his budget, the total cost including the uniform should be less than or equal to $154.

Hence, the inequality that represents this situation is:

[tex]\[ 8c + 12 \leq 154 \][/tex]

This inequality states that the cost of the uniform plus the cost of the classes must be less than or equal to Theo's budget. Solving for [tex]\( c \)[/tex] will give us the maximum number of classes Theo can attend without exceeding his budget.

Answer:

Ok so ppl it just A

Step-by-step explanation:

To solve this problem, we must first subtract 4 from both sides of the inequality. This gives us -2 ≥ -v. Next divide both sides by -1. Remember, when you divide by a negative in an inequality, it becomes necessary to flip the direction of the inequality symbol. Therefore, the answer to the inequality is 2 ≤ v, which is equivalent to v ≥ 2.

The number of cakes she can make is 9.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Stella has 6 pounds of chocolate. She will use 2/3 pounds of the chocolate to make one cake.

The number of cakes will be calculated as,

Number = 6 / ( 2 / 3 )

Number = ( 6 x 3 ) / 2

Number = 9

Therefore, the number of cakes will be 9.

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The approximate surface area of the sphere will be 707 yd^2

The steps are as follow:

r = 7.5 yd

Surface area of sphere = 4πr^2

Surface area of sphere = 4*π*(7.5)^2

Surface area of sphere = 706.85 yd^2

Surface area of sphere = 707 yd^2

So the approximate surface area of the sphere will be 707 yd^2

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The volume of the prism is 22.5 cubic inches.

To find the volume of the prism, we need to first find the area of the base and then multiply it by the height. In this case, the base is a 45-45-90 triangle with a leg of 5 inches. The area of a triangle is given by the formula 1/2 * base * height, so the area of the base is 1/2 * 5 * 5 = 12.5 square inches. The height of the prism is given as 1.8, so we can now calculate the volume by multiplying the area of the base by the height: 12.5 * 1.8 = 22.5 cubic inches.

The range of f(x) is a single value which is the y-coordinate of any point on the horizontal line representing f(x).

The range of a function is the set of possible values its output can have. In this case, the function f(x) is a horizontal line. Since f(x) is restricted to the portion between x = 0 and x = 20, inclusive, the range of f(x) is the set of all y-values within that range. Since the graph of f(x) is a horizontal line, the range of f(x) is a single value, which is the y-coordinate of any point on the line.

Based on the graph shown below, the range of f(x) include the following: B. { f(x)| –∞ < f(x) ≤ 4}

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following range:

Range = (-∞, 4] or {f(x)| –∞ < f(x) ≤ 4}

Complete Question;

What is the range of f(x)?

{ f(x)| –∞ < f(x) < ∞}

{ f(x)| –∞ < f(x) ≤ 4}

{ f(x)| 4 < f(x) < ∞}

{ f(x)| 0 ≤ f(x) < ∞}

The area that a dog can roam, attached to a 49-foot rope at the corner of a 42x51 foot garden, was initially calculated as a quarter-circle's area with mistakes acknowledged in the approach. The correct calculation involves more intricate geometrical considerations, considering the question's unique constraints.

To determine the area that a dog can wander, given it's attached to a 49-foot rope fastened to the outside corner of a fenced-in garden measuring 42 feet by 51 feet, we need to consider the shape of the area the dog can cover. The dog can cover a quarter-circle around each of two adjacent sides of the garden and a semi-circle along the side opposite the corner where the rope is fastened, provided the rope's length exceeds the garden's dimensions on those sides.

Calculating the area involves adding the areas of these three parts:

Therefore, the total area that the dog can wander is effectively the area of a quarter-circle with a radius of 49 feet. This can be calculated as:

Area = 1/4 * π * (49)^2 square feet

Calculating this gives an area of 1884.96 square feet (rounded to two decimal places).

However, upon reevaluation, it's clear that a mistake was made in the initial explanation; the correct approach is to consider not just a quarter-circle but also the additional areas the rope covers beyond the garden's dimensions.

The exact area that the dog can wander is [tex]{2401\pi} \)[/tex] square feet.

Identify the radius: The radius of the circle that the dog can wander is the length of the rope, which is 49 feet.

Calculate the area of the circle: Use the formula for the area of a circle, [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r = 49 \)[/tex] feet.

[tex]\[ A = \pi \times 49^2 \][/tex]

Compute [tex]\( 49^2 \)[/tex]:

[tex]\[ 49^2 = 2401 \][/tex]

Multiply to find the area:

[tex]\[ A = \pi \times 2401 \][/tex]

The exact area that the dog can wander is [tex]{2401\pi} \)[/tex] square feet.

This calculation confirms that the dog can wander an area of [tex]\( 2401\pi \)[/tex] square feet within the fenced-in garden while attached to the 49-foot rope.

Lance rolls a die 5 times

In a six sided dice, the even numbers are 2, 4  and 6. So 3 even numbers

the probability that he rolls an even number = [tex]\frac{3}{6} = \frac{1}{2}[/tex]

the probability that he rolls an even number all five times

= [tex]\frac{1}{2} *\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}= \frac{1}{32}[/tex]

So answer is [tex]\frac{1}{32}[/tex]

Calculate the cost per apple for large and small baskets, $0.39 per apple is the closest estimate.

To estimate the cost per apple, one must calculate the price of each apple in the large and small baskets, then average these amounts, resulting in approximately 44 cents per apple.

To find the cost per apple:

Calculate the cost per apple in the large basket: $22.95 / 59 apples = $0.39 per apple.

Calculate the cost per apple in the small basket: $8.95 / 18 apples = $0.50 per apple.

Compare the two costs: $0.39 is the closest estimate of the cost per apple.

Answer:

The correct option is C.

Step-by-step explanation:

In a dot plot, the number of dots above a number represents the frequency of that number.

From the given dot plot it is clear that number of dots for group R is 21 and the time taken by the students of groups R are

45, 50, 50, 55, 60, 60, 70, 75, 80, 85, 90, 90, 95, 100, 100, 105, 110, 110, 115, 120, 120

The average of the data is

[tex]Average=\frac{\sum x}{n}[/tex]

[tex]Average=\frac{45+50+50+55+60+60+70+75+80+85+90+90+95+100+100+105+110+110+115+120+120}{21}[/tex]

[tex]Average=\frac{1785}{21}[/tex]

[tex]Average=85[/tex]

From the given dot plot it is clear that number of dots for group S is 17 and the time taken by the students of groups S are

50, 55, 60, 60, 65, 70, 70, 80, 90, 90, 95, 100, 105, 110, 110, 115, 120

[tex]Average=\frac{50+55+60+60+65+70+70+80+90+90+95+100+105+110+110+115+120}{17}[/tex]

[tex]Average=\frac{1445}{17}[/tex]

[tex]Average=85[/tex]

The average time of both groups are same.

Since both groups show about the same average time, therefore the correct option is C.