Suppose two bicyclists start at the same location.
The first bicyclist rides due north and the other rides
due west. Find the speed that each bicyclist rode in
miles per hour if they are 8V2 miles apart after riding
for 2 hours at the same speed

The linear function with f values f(0) = -3 and f(7) = 11 is f(x) = 2x - 3

linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.

if f(0) = -3, it means at x = 0, f(x) = -3

and if f(7) = 11, it means at x = 7, f(x) = 11

So the Linear equation that will yield these results is f(x) = 2x - 3

In conclusion, the Linear function is f(x) = 2x - 3

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Answer:

B,C, and E

Step-by-step explanation:

Got it right on the assignment

Answer:

I think it's false

Step-by-step explanation:

Answer:

A rational expression is a ratio of two polynomials. The domain of a rational expression is all real numbers except those that make the denominator equal to zero.

Step-by-step explanation:

Answer:

(0,4)

Step-by-step explanation:

The y-intercept is 4

The given expression is 9x²y²z - 6x³y² + 3x³y²z². In order to rewrite the given expression as a product by pulling out the greatest common factor, we have to find the greatest common factor of the given terms.

The greatest common factor is the common factor that divides all the given terms.

Factors of each term are as follows:9x²y²z = 3 × 3 × x × x × y × y × z

6x³y² = 2 * 3 * x * x * x * y * y

3x³y²z² = 3 * x * x * x * y * y * z * z

So, the greatest common factor of all the given terms is 3x²y².

Hence, we can rewrite the given expression as a product by pulling out the greatest common factor.3x²y²(3z - 2x + xyz)

Therefore, 9x²y²z - 6x³y² + 3x³y²z² = 3x²y²(3z - 2x + xyz).

Hence, we have rewritten the given expression as a product by pulling out the greatest common factor.

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X is a normal distribution with mean 4 and standard deviation 8 (since the variance is 64), therefore P(X ≤ –5.2) is approximately 0.1251.

If X follows a normal distribution N(4,64), then it has a mean (μ) of 4 and a variance (σ²) of 64, with a standard deviation (σ) of 8. To find the probability P(X ≤ -5.2), we need to calculate the z-score for -5.2 and use the standard normal distribution table.
Substituting in the values, we get:
z = (-5.2 - 4) / 8
z = -1.15
Now, we can look up the probability of a standard normal distribution with a z-score of -1.15 using a table or calculator, which gives us:
P(Z ≤ -1.15) = 0.1251
Therefore, P(X ≤ –5.2) is approximately 0.1251.

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Answer:

1

Step-by-step explanation:

1+3 = 4  4*7 = 28

it's 1 because 28/7 = 4 and you add 3 to the number so 1 + 3 = 4 * 7 = 28 is correct.

The probability that a sample of 4 bags will have a mean weight of fewer than 9.8 pounds will be 0.05.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}\)

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

Given that, a fertilizer manufacturer produces fertilizer in 10-pound bags with a standard deviation of 0.24 pounds per bag, Normally, the bag weights are distributed.

Given the data in the question;

μ= 10-pound bags

standard deviation s= 0.24 pounds

sample size n = 4

Typically, the bag weights are distributed as follows:

p( x' less than 9.8 ) will be;

p(  (x'-μ_x' / s_x')   <   (9.8-μ_x' / s_x')  )

As we know that;

μ_x' = μ_x = 10

and s_x' = s_x/√n = 0.24/√4

Put the value as

p(  z  <  ( (9.8 - 10) / (0.24/√4)  )

p(  z  <  -0.2 / 0.12   )

p(  z  <  -1.67   )

{ From z-table }

⇒ p(  z  <  -1.67   ) = 0.0475 ≈ 0.05

Thus, the probability that a sample of 4 bags will have a mean weight of fewer than 9.8 pounds will be 0.05.

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Answer:

C. 13,248 square units

Step-by-step explanation:

You need to use the Pythagoras theorem to find the missing side.
a^2+b^2=c^2
c^2-a^2=b^2
115^2-69^2=92^2
92+100=192
192*69=13,248

Answer:

$8303.75

Step-by-step explanation:

(6000x1.025^2)+2000=8303.75

There are approximately over 60 million shipping containers in the world. Containers are stacked and arranged in these ports, creating an impressive sight and highlighting the scale of global trade.

Shipping containers are standardized metal boxes used for transporting goods by sea, rail, or road. They come in various sizes, including 20-foot and 40-foot lengths. These containers have revolutionized global trade, allowing for efficient and secure transportation of goods across long distances. While exact numbers are challenging to determine due to factors such as container movement and usage, estimates suggest that there are over 60 million shipping containers worldwide. This vast quantity of containers enables the global economy to function smoothly by facilitating the movement of goods between countries and continents.

The extensive use of shipping containers has led to the establishment of container ports and specialized container ships that can accommodate large numbers of containers.Moreover, repurposing shipping containers for alternative uses, such as modular homes or pop-up shops, has gained popularity in recent years, demonstrating the versatility and durability of these units.

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The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

Answer:

$240

Step-by-step explanation:

this would be solved using simultaneous equation

let c = cost of cds

d = cost of dvds

two equatiions can be derived from the question

5d + 9c = 285 eqn 1

5d + 5c = 225 equation 2

subtract equation 2 from 1

4c = 60

c = 15

substitute for c in eqn 1

5d + 9(15) = 285

5d = 150

d = 30

5(30) + 6(15) = 240

Answer:

i dunno

Step-by-step explanation:

hard man

An obtuse triangle and right angle triangle can always be used as counter examples to the given statement.

What is acute angle?

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle

What is obtuse angle?

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

What is right angle?

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles..

Hence, an obtuse triangle and right angle triangle can always be used as counterexamples to the given statement " All angles in a triangle are acute".

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After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

35, 56, x=4

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

First, convert 1 1/3 to improper fraction:

1 1/3 = 4/3

Second, make denominator the same by multiplying 4/3 by 2/2:

4/3 * 2/2 = 8/6

Third, subtract:

8/6 - 5/6 = 3/6

Fourth, simplify:

3/6 = 1/2

The correct answer for the difference between \(1\dfrac{1}{3}\)  and \(\dfrac{5}{6}\)  is  \(\dfrac{1}{2}\) .

Given expression:

\(1\dfrac{1}{3} - \dfrac{5}{6}\)

convert \(1\dfrac{1}{3}\)  to an improper fraction:

\(1\dfrac{1}{3} = \dfrac{3*1 + 1}{3}\)

= \(\dfrac{4}{3}\)

Now, the expression becomes:

\(\dfrac{4}{3} - \dfrac{5}{6}\)

To subtract these fractions,

The common denominator is 6.

Rewrite the fractions with the common denominator:

\(\dfrac{4}{3}*\dfrac{2}{2}\)

= \(\dfrac{8}{6}\)

The expression becomes:

\(\dfrac{8}{6} - \dfrac{5}{6}\)

Subtract, the numerators while keeping the common denominator:

= \(\dfrac{8-5}{6}\)

= \(\dfrac{3}{6}\)

Divide  numerator and denominator by greatest common factor (which is 3):

3 ÷ 3 = 1

6 ÷ 3 = 2

= \(\dfrac{1}{2}\)

The correct answer is for \(1\dfrac{1}{3} - \dfrac{5}{6}\)   is  \(\dfrac{1}{2}\).

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Answer:

24

Step-by-step explanation:

120 minus 80% = 120 times 20% (fractions division method)

120 times 20% = 120 times 0.2 (simplify)

120*0.2 = 24, so the answer is 24

The cost of the labor per hour x 122.18

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

The equals sign is a part of mathematical expressions known as equations. Often, algebra is used in equations. When a calculation requires an exact number but you don't know it, algebra is utilized.

both identities and conditional equations. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

655.75-167

=488.75

488.75 divided by 4

488.75/4

= 122.18

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2(x+1)+4

Distributive property : According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

solve equation by using distributive property we should use laws of this property that are as follows:

Expand the equation. Multiply (distribute) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set. Combine like terms.

2(x + 1) + 4 = 8

2(x)+2(1)+4=8

2x+2+4=8

2x+6=8

2x=8-6

2x=2

x=2/2

x=1

so final conclusion is Option A  2(x+1)+4=8 is the right answer

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Answer:

The equation of the lines with the given point does not have a y-intercept of 4 but has a y-intercept of -4.

Step-by-step explanation:

y-intercept is 4

addition ordered pairs on the line are (2, -2), (4, 0), (6, 2), (8, 4)

Find the slope using two of the points: (2, -2), (4, 0).

Slope = (change in the y values)/(change in the x values0

Slope = [0 -(-2)]/ (4 - 2) =   2/ 2 = 1

Checking to see if the y-intercept is 4 substituting  slope (m) = 1 and (2, - 2)

      y = mx + b

     -2 = 1(2) + b

     -2 = 2 + b

  -2 - 2 = b

    -4 = b   so we know that the y-intercept is not 4 but it is -4.

Now write the equation of the line using a slope = 1 and y-intercept of -4

y = mx + b

y = x - 4

Next check the other points into the equation of the line to see if the equation is correct.

x = 2   did y = -2 ?    y = x - 4;   y = 2 - 4 ; y = -2     point (2, -2) works.

x  = 4   did y = 0?     y = x - 4;  y = 4 - 4;  y = 0       point (4,0)  works.

x = 6    did y = 2?     y = x - 4;  y = 6 - 4; y = 2         point (6, 2) works.

x = 8     did y = 4?     y = x - 4; y = 8 - 4;  y = 4        point (8, 4) works.

The basis of the image of T is formed by the set of vectors in the x-y plane, by using the concept of Linear transformation.

For the given question, we will use the concept of Linear transformation.

A linear transformation is a function that maps one vector space to another vector space, and that preserves the vector space operations like addition and scalar multiplication. It is also known as linear mapping or linear operator and has the property that

T(ku) = kT(u) and T(u + v) = T(u) + T(v) ∀ vectors u and v and all scalars k.

There are different methods to find the basis of ker T, and im T, such as using the rank-nullity theorem, finding the reduced row echelon form of the matrix representation of T, or finding the eigenvectors and eigenvalues of T.

Let's find the basis of ker T, and the basis of im T for the given cases.

(a) T: P2 → R2; T(a + bx + cy2) = (a, b)
The kernel of T is the set of polynomials in P2 such that T(p) = (0, 0), or equivalently, a = b = 0.

Thus, the basis of ker T is {c2}, the set of polynomials of degree less than or equal to 1.

The image of T is the set of vectors in R2 that can be written as (a, b) = T(p) for some polynomial p in P2.

Thus, the image of T is the entire R2, and the basis of im T is {(1,0), (0,1)}.

(b) T: P2 → R2; T(p) = (p(0), p(1))
The kernel of T is the set of polynomials in P2 such that T(p) = (0, 0), or equivalently, p(x) = 0 for all x.

Thus, the basis of ker T is {x(x - 1)}.

The image of T is the set of vectors in R2 that can be written as (a, b) = T(p) for some polynomial p in P2.

Thus, the image of T is the set of linear combinations of the two vectors (1,0) and (0,1), which form a basis of im T.

(c) T: R3 → R3; T(x,y,z) = (x + y, x + y, 0)
The kernel of T is the set of vectors in R3 such that T(x, y, z) = (0, 0, 0), or equivalently, x + y = 0 and z = 0. Thus, the basis of ker T is {(1,-1,0), (0,0,1)}.

The image of T is the set of vectors in R3 that can be written as T(x, y, z) = (a, b, 0) for some a and b.

Thus, the image of T is the set of vectors in the x-y plane, which form a basis of im T.

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Answer:

7/4

Step-by-step explanation:

i am sooo sure that  the answer is 1.75