John took 30 minutes to bicycle to his grandmother’s house, a total of 2.5 kilometers. What was his speed in km/hr?

The equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.

How simplification method work?

In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.

According to the question, the given equation can be simplified by using simplification method and it is written below:

The given equation is: 3x - 6 = 18

3x = 18 + 6 = 24 ⇒ 3x = 24

Similarly, 3x - 6 = 18

3(x - 2) = 18

Hence, the equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.

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IN OTHER WORDS WE ARE LOOKING FOR WHOLE NUMBERS BETWEEN -6 AND 2

[tex] - 5 \\ - 4 \\ - 3 \\ - 2 \\ - 1 \\ 0 \\ 1[/tex]

ATTACHED IS THE SOLUTION

Answer:

1,0,-1,-2,-3,-4,-5

Step-by-step explanation:

The most appropriate choice for HCF of two numbers will be given by -

Maximum number of performers in each row so that all the rows are equal in length = 8

What is HCF?

HCF means Highest Common Factor. HCF of two numbers a and b is the largest number that is divides both a and b.

Number of instruments  = 24

Number of flag bearers = 16

Maximum number of performers in each row so that all the rows are equal in length = HCF of 24 , 16

[tex]24 = 2^3 \times 3\\16 = 2^4[/tex]

HCF = [tex]2^3[/tex] = 8

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Answer: f(3) = 0.84375

Step-by-step explanation:

f(3) is asking for the value of the function when x = 3, not multiplying f by 3. (f(x) is basically the output, y)

So we just plug in 3 for x and simplify (use PEMDAS)

f(3) = 2(0.75)^3

f(3) = 2(0.421875)

f(3) = 0.84375

Answer:

[tex]\frac{27}{32}[/tex]

Step-by-step explanation:

It may be a bit easier to represent 0.75 as a fraction, since we can use the following property of exponents: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex]

We can represent 0.75 as: [tex]\frac{3}{4}[/tex]

And substituting this into the function we get: [tex]f(x)=2(\frac{3}{4})^x[/tex]

calculating the value when x=3, we get: [tex]f(3)=2(\frac{3}{4})^3[/tex]

using the property previously stated we get: [tex]f(3)=2(\frac{3^3}{4^3})[/tex]

Raising each value to the exponent we get: [tex]f(3)=2(\frac{27}{64})[/tex]

When we multiply by two, we can simplify by splitting up 64, into two factors: 2 and 32, to get: [tex]\frac{2*27}{32*2}[/tex]

From here it's easy to see that we can cancel out the values 2, to get: [tex]\frac{27}{32}[/tex]

Which is our answer!

Answer: t> -4/95

Step-by-step explanation: times both sides by 10(just make the calculation easier, no need to do that)

5t+1<100t+5

-95t<4

t > -4/95

Let f(x) = 9x - 8. Find (f o f)(1).​

we know that

(f o f)(1).=f(f(1))

step 1

find f(1)

f(1)=9(1)-8

f(1)=1

substitute

f(f(1))=f(1)=1

therefore

the answer is 1

The slope of the line to represent the volume of water in a pool over time would described as -10

From the given table we have to choose points to find the slope of the line

The domain is defined as the set of possible inputs of the function.

The range is defined as the set of all possible outputs of the function.

The slope of the line is the change in y coordinate with respect to the change in y coordinates

Slope of the line m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Where m is the slope of the line

[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are the coordinates of the two points

We have to choose two points

The two points (2,44) and (4,26)

m = [tex]\frac{26-46}{4-2}[/tex]

m = -20/2

m = -10

Hence, the slope of the line to represent the volume of water in a pool over time would described as -10

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The ratio between cups of beans and cups of rice is 10/13 . Option C

A ratio can described as an ordered pair of numbers, like y and z, that is written mathematically in the form y / z where the denominator of the fraction is not equal to zero.

It is known to describe the number of times an element or number contains another number proportionally.

It is also seen as the comparison of two quantities, elements or numbers that has the same units and likewise, explains how much one of the elements or quantity is found in the another one.

This is done based on their sizes or magnitudes.

A proportion is a mathematical equation with two ratios set equivalent or equal to each other.

Given that;

Beans = 2 1/ 2 cups

Rice = 3 1/4 cups

Convert to mixed fractions;

Beans = 5/2

Rice = 13/4

Now, divide the cups of beans by that of rice;

= 5/ 2 ÷ 13/4

= 5/2 × 4/13

= 10/13

Hence, the ratio is 10/13

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Using vertical angles, it is found that:

A. The solution for y is of y = 4.

B. The angle measures are given as follows:

If two angles are opposite by the same vertex in crossing segments, these angles are called vertical angles, and they are congruent, that is, they have the same measure.

In the context of this problem, the angles of 6y + 42 and of 66 are vertical, hence the value of y is calculated as follows:

6y + 42 = 66

6y = 24

y = 24/6

y = 4.

Angles A and C are supplementary, meaning that the sum of their measures is of 180º, hence:

<C + 66º = 180º

<C = 180º - 66º

<C = 114º.

Angles C and D are vertical, hence the measure of angle D is calculated as follows:

<D = 114º.

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Answer:

This is a 30 60 90 triangle. They are saying the hypotenuse is 3x + 6 and the shortest side is 8x - 4. In a 30 60 90 triangle, the hypotenuse is 2 times the short side meaning that/

3x + 6 = 16x - 4

Now we can solve...

10 = 13x

x= [tex]\frac{10}{13}[/tex]

Answer:

3/4

Step-by-step explanation:

9/12  Divide the top and bottom by 3

3/4

The probability that rose identifies all 3 cards in the correct order is 1/132,600 by the concept of permutation.

It is the separate arrangements of a given number of associates taken all at once, or some of them, or just a few of them. There are two possible meanings, AB and BA, for instance, if we have the two elements A and B.

Following the arrangement of 'r' items from a total of 'n' elements, the number of permutations is,

nPr = n! / (n – r)!

Here to obtain the probability in correct order use permutation formula

Recall that, Probability is calculated as favorable outcomes divided by all possible outcomes.

Favorable number of outcomes = 1 (as only one order is correct)

Total outcomes = 52p3 (since 3 cards to be arranged from pack of 52)

So, the probability of rose identifies all 3 cards in correct order =1/52p3

Probability = [tex]\frac{1}{52!/(52-3)!}[/tex]

Probability = 49! /52!

Probability = 49! /52*51*50*49!

Probability = 1/52*51*50

Probability = 1/132,600

Therefore, the probability that rose identifies all 3 cards in the correct order is 1/132,600.

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The distance between the lake and campground  is 48 miles.

Given

The distance between the campground and the entrance is 2

The actual distance between them is 8 miles

Hence the scale is 2 for 8 miles

Also, Distance on the map between campground and lake is 12 inch.

Let us say actual distance is x

There fore we can form equation as

2x = 12x18

2x = 216

x=48

Hence the actual distance between campground and lake is 48 miles.

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From the graph, we can see that the set of ordered pairs which belongs to the line are

D). (2, 100), (3, 150), (5, 250)

Because x-axis is the first coordinate and y-axis is the second coordinate. In options B and C, they are

arranged in the wrong place. In option A, point (3,125) doesn´t belong to the line.

Answer:

1187.49

Step-by-step explanation:

[tex]P(40)=0.023(40)^3-0.289(40)^2+3.068(40)+55.170=1187.49[/tex]

As per given by the question,

There are given two figure on coordinate grid, figures 1 and 2.

Now,

From concept of similar figure:

Similar figure means, that have the same shape and exactly the same in every way, on the other hand;

The similar figure means they are same shape but not the same size, then these figure is also called similar figure.

Now,

From concept of the congruent figure:

The congruent means, that two figure exactly the same that means, we can say that they are congruent, when both figure have same shape and same size.

So,

According to both concept, similar and congruent;

The given figure 1 and 2 is simililar, because of same shape. But due to different size, both figure have not congruent.

So, the given figures 1 and 2 is similar, but not congruent.

Hence, the option first is correct.

Using trigonometric ratio. SOHCAHTOA

An acute triangle is a triangle with three acute angles, whereas an obtuse triangle is a triangle with one obtuse angle and two acute angles.

An obtuse angle is a angle which is more than 90°.

In our problem, the triangle has a 110° angle, and 110°>90°; therefore, the answer is obtuse triangle

Answer:

option d is the correct answer

Given the expression below

Step 1: Using PEMDAS rule

P=> Parenthesis

E=>Exponent

M=>Multiplication

D=>Division

A=>Addition

S=> Subtraction

From the rule above, we will start our simplification with the parenthesis

Step 1: simplify (5-4)

Step 2: Expand 2(1)=> 2x1, then simplify (6-2(1))

Step 3: Expand 6(4)=>6 x 4

Step 4: Add 8 and 24

Hence, the final answer is 32

Answer: your answer would be 32

Step-by-step explanation:

using PEMDAS we would first go by parentheses and use the order by each step.

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

Given :

The statistician reported that the mean serve speed was 100 miles per hour

the standard deviation of the serve speeds was 15 mph

Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric

To find :

What percentage of the player's serves were between 115 mph and 145 mph?

Solution :

μ =100

σ = 15

P ( 115 < x <145)

= P ( [tex]\frac{115-100}{15}[/tex] <  x-μ /6 <[tex]\frac{145-100}{15}[/tex] )

= P ( [tex]\frac{15}{15}[/tex] < z < [tex]\frac{15}{15}[/tex] )

= p ( 1<z<3)

= p( z<3)-p(z-1)

=0.9987-0.8413

=0.1574

p ( 115<xx<145)= 15.74 %

p( 115<x<145)= approximately 16%

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

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In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.

We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;

420t + 5750

where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;

t = 2006 - 1995

t = 11 years

Thus;

f(11) = 420(11) + 5750

f(11) = 10370 dollars

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Answer:

The distance between two points (x₁,y₁) and (x₂,y₂) on the coordinate plane is d=√((x₂-x₁)²+(y₂-y₁)²)

√(8 - 3)² + (7 - 5)² = √29 ≈ 5.3851648071345

We have to write an equation from the word problem,

Four subtracted from the product of 5 and a number is 51

Let's break it down:

--- product of 5 and a number can be written as,

--- four subtracted from "product of 5 and a number" can be written as,

^^ All this is equal to 51, so we can write,

To find the unknown number, we solve the above equation. The steps are shown below:

Answer:

good jb

Step-by-step explanation:

Inequality: [tex]x-7\ge 15[/tex]

Solution: [tex]x\ge 22[/tex]

Inequality is a mathematical statement which depicts the relation between two or more mathematical variable or quantities which involves in relation which is not equal or inequal.

Given the statement is "A number decreased by 7 is at least 15"

Let the number be the variable x.

Now decreased by 7 = x-7

Suitable inequality sign for at least statement is [tex]\ge[/tex]

So the required inequality is given by,

[tex]x-7\ge15[/tex]

Solving the same we get,

[tex]x-7+7\ge 15+7[/tex]

[tex]x\ge 22[/tex]

Thus the number is [tex]x\ge 22[/tex]

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Given:

There is a rectangular prism shape water tank given with 23yd 15yd anf 4yd measurements

Required:

A) We need to find the volume of tank in cubic ft

B) 18.8 cubic ft need 1 salt bag then we need to find to total needed salt bag

C) $4.65 per bag then find total cost

Explanation:

first pf all we need to convert given measures in feet from yd

A)

Volume

B)

18.8 cubic ft need 1 bag

then

37260 cubic ft need x

C)

Cost for 1 bag is $4.65

then

cost for 1982 bags is y

Final answer:

A) volume of tank in cubic ft is 37260

B) 18.8 cubic ft need 1 salt bag then we need total 1982 needed salt bags

C) $4.65 per bag then total cost is $9216.3

Anlges A and D are right angles becuase they measure 90

Angle C is Acute because it is smaller than 90

Angle B is Obtuse because it is grather than 90

Answer:

See below

Step-by-step explanation:

Slope of given line is 1      y = (1) x + 2

 parallel line has same slope

    so it will start to look like this    y = (1) x   + b

        sub in the point 5,7 to find b = 2

final answer y=x+2

Answer:

q=1

Step-by-step explanation:

2(q+4)=10

q+4=5

q=1

:]

Answer:

3

Step-by-step explanation:

2 x 3 6 4 10