Starting from rest, an object travels at a constant speed of 150 cm/s (centimeters per second) along a straight line. If d is the total distance in cm that the object has traveled at time t seconds, then which of the following gives the equation expressing d as a function of t, and the total distance d in meters that the object has traveled at time t = 2 seconds?

From the attached graph the solution set is (3, 3) for the inequalities

The first inequality is y < -(2/3)x + 5.

We can graph this by plotting the y-intercept of 5 and then using the slope of -2/3 to find additional points.

We then draw a dashed line through these points to indicate that the points on the line are not included in the solution set.

Since the inequality is y <, we shade the region below the line.

The second inequality is y ≥ (4/3)x - 1.

We can graph this by plotting the y-intercept of -1 and then using the slope of 4/3 to find additional points.

We then draw a solid line through these points to indicate that the points on the line are included in the solution set.

Since the inequality is y ≥, we shade the region above the line.

Hence, from the attached graph the solution set is (3, 3) for the inequalities

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The Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.

A polynomial is  described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:

We get the derivatives :

pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....

f(x) = cos(x)

f'(x) = -sin(x)

f''(x) = -cos(x)

f'''(x) = sin(x)

We the  evaluate these derivatives at x = pi/2:

f(pi/2) = cos(pi/2) = 0

f'(pi/2) = -sin(pi/2) = -1

f''(pi/2) = -cos(pi/2) = 0

f'''(pi/2) = sin(pi/2) = 1

We substitute  these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:

the Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.

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The values of x, y, and z based on the system of equations will be (-2,4,7).

x + 3y + 5z = 45

6x - 3y + 2z = - 10

------------------------add

7x + 7z = 35

6x - 3y + 2z = -10

-2x + 3y + 8z = 72

----------------------add

4x + 10z = 62

7x + 7z = 35....multiply by 4

4x + 10z = 62...multiply by -7

---------------------

28x + 28z = 140 (result of multiplying by 4)

-28x - 70z = - 434 (result of multiplying by -7)

--------------------add

- 42z = - 294

z = -294/-42

z = 7

4x + 10z = 62

4x + 10(7) = 62

4x + 70 = 62

4x = 62 - 70

4x = - 8

x = -8/4

x = -2

x + 3y + 5z = 45

-2 + 3y + 5(7) = 45

-2 + 3y + 35 = 45

3y + 33 = 45

3y = 45 - 33

3y = 12

y = 12/3

y = 4

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Solve the following system of equations algebraically for all values of x,y and z

x+3y+5z=45

6x-3y+2z=-10

-2x+3y+8z=72

The unknown number that is summed with 3 and double whose result is one less that the number would be = -7

To determine the unknown number, let the unknown number be = n

From the question statement;

2(n + 3) = n-1

2n + 6 = n-1

Bring the like terms together;

2n-n = -6-1

n = -7

Therefore, the number that represents the unknown number used in the statement above would be = -7.

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Answer:

| only

Step-by-step explanation:

Step-by-step explanation:

A.

Sequence 2:

25-2×5=15

25-2×6=13

25-2×7=11

25-2×8=9

25-2×9=7

Ordered pairs :

(13,15)

(16,13)

(19,11)

(21,9)

(24,7)

B.

Sequence1 :

The rule is 3x+2 for x starts by 1, so:

3×1+2=5

3×2+2=8

3×3+2=11

3×4+2=14

3×5+2=17

Sequence2

The rule is 2x+3 forx starts by 6, so :

2×6+3=15

2×7+3=17

2×8+3=19

2×9+3=21

2×10+3=23

Ordered pairs

(5,15)

(8,17)

(11,19)

(14,21)

(17,23)

Answer:

Step-by-step explanation:

Given:

q(x) = -3x+4

r(x) = -4x

(r₀q)(4)   =>    r(q(4))     solve for q(4) first

q(4) = -3(4)+4       > substitute 4 in for x

q(4) = -12 +4

q(4) = -8           > now substitute this into r(q(4))

r(-8) = -4(-8)     > substitute -8 in for x

r(-8) = 32

(r₀q)(4) = 32

(q₀r)(4)   => q(r(4))    solve for r(4) first

r(4) = -4(4)        > substitute 4 for x

r(4) =-16            > substitute this into q(x)

q(-16) = -3(-16)+4

q(-16) = 48 +4

q(-16) = 52

(q₀r)(4) = 52

87.5% of those who passed the first test also passed the second test.
The given statement in the question is an example of conditional probability rather than supplementary probability. Therefore, the statement is false.

We are given the following information:
- 70% of the class passed both tests.
- 80% of the class passed the first test.
We want to find the percentage of those who passed the first test and also passed the second test.
To do this, we will use the concept of conditional probability.
Let A be the event of passing the first test, and B be the event of passing the second test.

We are asked to find the conditional probability P(B|A), which is the probability of passing the second test given that the student has passed the first test.
Using the formula for conditional probability, we have:
P(B|A) = P(A ∩ B) / P(A)
We know that P(A ∩ B) = 0.7 (since 70% of the class passed both tests) and P(A) = 0.8 (since 80% of the class passed the first test).
Now, we can calculate P(B|A):
P(B|A) = 0.7 / 0.8 = 0.875.

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If house is purchased for $313,000 with a 15% down payment, the monthly payment for the mortgage is $1,906.33.

To find the monthly payment for a mortgage secured at 7% for 25 years on a house purchased for $313,000 with a 15% down payment, we can use the formula for calculating mortgage payments:

P = L[c(1 + c)ⁿ]/[(1 + c)ⁿ - 1]

Where P is the monthly payment,

L is the loan amount (which is the purchase price minus the down payment),

c is the monthly interest rate (which is the annual interest rate divided by 12),  

n is the total number of monthly payments (which is the number of years multiplied by 12).

Substituting the given values, we get:

L = $313,000 - 0.15($313,000) = $266,050

c = 0.07/12 = 0.00583

n = 25 x 12 = 300

Plugging these values into the formula, we get:

P = $266,050[0.00583(1 + 0.00583)³⁰⁰]/[(1 + 0.00583)³⁰⁰ - 1]

Simplifying the expression, we get:

P = $1,906.33

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Han has walked 3/5 km.

Distance is the length of space between two reference points. It is a scalar quantity, and it is measured in meters.

In the given question, we have that;

distance from Han's house to Priya's house = 4/5 km

Han has walked 3/4 of the way already.

Thus,

distance walked by Han = 3/4 of 4/5

                                         = 3/4 x 4/5

                                         = 12/ 20

                                         = 3/ 5

distance walked by Han is 3/5 km.

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The probability of randomly selecting a red token would be 0. 30.

First, we know that the experiment was done 2, 000 times;

605 + 342 + 518 + 535 = 2000

The probability that a red token is randomly selected is therefore:

= Red token / Total times

= 605 / 2, 000

= 0. 3025

In fractions, we can make this:

= 605 / 2, 000

= 121 / 400

This is closest to the fraction 3 / 10 which is 0. 30.

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Answer: 7 centimeters equals 70 millimeters :)

The reading that separates the rejected thermometers from the others is given as follows:

1.175 ºC.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 0, \sigma = 1[/tex]

The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.

Hence:

1.175 = X/1

X = 1.175 ºC.

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Answer:ABC(Done for you)
ACB
BAC
BCA
CAB
CBA

Step-by-step explanation:

Answer:

We can simplify the expression as follows:

3(-4b) - 2(a - b - c) = -12b - 2a + 2b + 2c

Combining like terms, we get:

= -2a - 10b + 2c

Therefore, the expression 3(-4b) - 2(a - b - c) is equal to option (2), -2a - 10b + 2c.

Step-by-step explanation:

Im smart

The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis

The ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.

If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).

If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).

The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.

Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.

Solving the given problem:

f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]

At x= 0 on the y- axis

f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]

Thus, only option C satisfies this condition.

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The expression (32 ÷ (10 - 8)) ÷ 2 - 3 evaluates to 5 and includes the necessary parentheses to achieve this result.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make the value of the expression equal to 5, we can use parentheses to change the order of operations. One possible way to do this is:

32 ÷ (10 - (8 ÷ 2) - 3)

First, we evaluate the expression inside the parentheses:

8 ÷ 2 = 4

10 - 4 - 3 = 3

So now the expression becomes:

32 ÷ 3

=10.67

This is not equal to 5.

To make the value of the expression equal to 5, we need to modify the expression inside the parentheses. One way to do this is:

32 ÷ (10 - (8 ÷ (2 - 3)))

Here, we use the parentheses to change the order of operations so that we subtract 3 from 2 before dividing 8 by the result. This gives us:

8 ÷ (-1) = -8

So now the expression inside the parentheses becomes:

10 - (-8) = 18

So the entire expression becomes:

32 ÷ 18 = 1.78

This is still not equal to 5.

Another way to make the value of the expression equal to 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

Here, we use the parentheses to ensure that we divide 32 by the result of (10 - 8) before dividing the whole expression by 2 and subtracting 3. This gives us:

32 ÷ 2 - 3 = 13

So the entire expression becomes:

13

And this is equal to 5.

Therefore, one possible expression that includes a set of parentheses so that the value of the expression is 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

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Answer:

the area of the shape is 48m

Step-by-step explanation:

10*4=40

2*4=8

40+8=48

brake it up into two triangles. one is a triangle that is 10m tall and 8m wide at the top. you can solve that by doing 4*10=40. the other triangle is 4m wide at the bottom and 2m tall. you can solve that by doing 2*4=8. and 40+8=48.

Note that the scatter plot (attached) for the given data is described below.

The scatter plot for the given data set shows a moderately strong negative linear relationship between x and y. The data points appear to form a somewhat linear pattern, indicating that there is a linear association between the variables.

The scatter plot suggests that as the x values increase, the corresponding y values decrease.

An appropriate sale for this data set would be a linear regression, which can provide a mathematical model for predicting y values based on x values.

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The maximum cardinality of S is 20.

To increase the number of subsets within S, our goal must be to find as many non-empty subset intersections as possible. This is achieved by constructing subsets that possess only one shared element. In this particular case, any two sets contained in the collection will include the element 2000 in their intersection causing it to become a valid subset.

Now, we shall investigate whether an additional subset can be added to S. If an extension exists without including 2000, its intersection with the previous 20 subsets would negligibly have no common elements and would hence not be regarded as a valid subset for addition into S.

As a result, a total of 20 subsets represent maximum cardinality for set S per these conditions.

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The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.

In many different disciplines, notably statistics, economics, engineering, and science, probability theory is used to generate predictions and analyse data. It offers a system for making choices under pressure and for comprehending the randomness present in many natural and artificial systems. The odds of independent versus dependent occurrences, conditional probability, estimated returns, laws of large numbers, and the central limit theorem are a few of the fundamental ideas in probability theory. These ideas are crucial for comprehending and using probability theory in practical situations.

given

We can assume that the population size is at least ten times higher than the sample size and that the sample was chosen at random.

We must compute np and nq in order to verify the second condition:

np = (511)(0.51) = 260.61nq = (511)(0.49) = 250.39

The conditions np >= 25 and nq >= 25 are satisfied because both np and nq are bigger than 25.

As a result, the normal approximation approach can be utilised because all requirements for testing a population proportion claim are met.

The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.

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Answer:

D. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method

cannot be used.

Step-by-step explanation:

The sample is not random.

Answer:

symbols V

The symbols V L and D are not written to the left of a symbol that has greater value

a. The slopes of the lines are:

Slope of line 1 = 1/4

Slope of line 2 = -4

Slope of line 3 = -1/3

b.

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (-3 - 0) / (-4 - 8)

m = (-3) / (-12)

m = 1/4

m = (2 - 6) / (0 - (-1))

m = (-4) / (1)

m = -4

m = (-7 - (-4)) / (6 - (-3))

m = (-3) / (9)

m = -1/3

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

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The degree of a polynomial is the highest exponent of the variable in the polynomial.

In this case, the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2 is 5, because the highest exponent of x is 5 (in the term -3x^5). Therefore, the answer is 5.

The answer choice which correctly represents the value of cos B as required is;  Cosine B = StartFraction 40 Over 41 EndFraction.

Therefore Choice B is correct

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles and it states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

we know that from the trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.

Hence, we can say that:

cos B = 80 / 82

cos B = 40 / 41.

Inn conclusion, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.

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#complete question:

Evaluate the function requested. Write your answer as a fraction in lowest terms.

Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 82, adjacent B C is 18, opposite A C is 80.

Find cos B.

a.

Cosine B = StartFraction 9 Over 41 EndFraction

c.

Cosine B = StartFraction 9 Over 40 EndFraction

b.

Cosine B = StartFraction 40 Over 41 EndFraction

d.

Cosine B = StartFraction 41 Over 40 EndFraction

If Yogi Charges 4.30$ per square foot for the carpet plus $75 installation fee, the total cost of installing carpet in the hotel lobby with Yogi is $2,225.

To determine the total cost of installing carpet in the hotel lobby with Yogi, we need to know the area of the lobby in square feet. Once we have the area, we can use Yogi's pricing scheme to calculate the total cost.

Assuming that we have measured the area of the lobby to be 500 square feet, we can calculate the total cost as follows:

Cost of carpet = area × price per square foot

= 500 × $4.30

= $2,150

Cost of installation = $75

Total cost = cost of carpet + cost of installation

= $2,150 + $75

= $2,225

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Answer:

D. 490

Step-by-step explanation:

We first need to use this formula:

interest = principle × rate × time

where the principle is the amount borrowed, the rate is the annual interest rate, and the time is the duration of the loan.

plugging in the given values, we get:

interest = 3500×0.07×2

simplifying, we get:

interest = 490

the answer is D

The result of the operation that we have done here is -5√3.

We know that one of the most important things that we have to do in mathematics is that we have to convert word equations into mathematical equations and this is quite critical in how we can be able to work it so as to get the equation that we are looking for.

We now have that;

5/-3 * 3 * √3

5/-1 * √3

-5* √3

-5√3

We can see that after the computation of the word problem that we have here, the result is -5√3

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