Write a linear equation for the following table.
x = number
y = cost
0
15
35
55
75
95
y =
4
8
12
16
X +

The solution to the system of equations is (a) (1, 0)

From the question, we have the following parameters that can be used in our computation:

The graph

The point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (1, 0)

This means that

x = 1 and y = 0

Hence, the solution to the system of equations is (a) (1, 0)

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The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.

To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:

10f - 5f + 8 + 6g + 4

Combining the terms with 'f', we have:

(10f - 5f) + 8 + 6g + 4

This simplifies to:

5f + 8 + 6g + 4

Next, we can combine the constant terms:

8 + 4 = 12

Thus, the simplified expression is:

5f + 12 + 6g

This expression is equivalent to 10f - 5f + 8 + 6g + 4.

In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.

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The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.

To complete the given number sequence, let's analyze the pattern and identify the missing terms.

Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:

The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.

Using this pattern, we can determine the missing terms as follows:

To obtain the third term, we add 2 to the second term:

7 + 2 = 9

To find the fifth term, we add 3 to the fourth term:

16 + 3 = 19

To determine the seventh term, we add 4 to the sixth term:

__ + 4 = 23

Therefore, the missing terms in the sequence are 9, 19, and 23.

By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.

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The measure of angle of arc UB is 46°

An arc is a part of the circumference.

If two arcs in circles with equal radii have the same length, then their central angles (and measures) will be equal.

To find the measure of angle of arc UB, we use the theorem that says;

angle I = 1/2( angle ZC - angle UB)

angle I = 48°

angle ZC = 142°

Therefore ;

represent angle UB by x

48 = 1/2( 142-x)

142 - x = 96

x = 142 -96

x = 46°

Therefore the measure of angle of arc UB is 46°

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Answer:

It's 18.37

Step-by-step explanation:

I'm smart trust me.

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

The degree of f(x) is 5, and the leading coefficient is negative. There are 3 distinct real zeros and 2 relative maximum values.

From the graph of a function, the zeros of the function are the x-intercepts, that is, the values of x for which the graph crosses or touches the x-axis.

The function in this problem has three distinct zeros, given as follows:

Hence the degree of the function is given as follows:

2 x 2 + 1 = 5.

The leading coefficient is negative, as the function has an odd degree, but increases to left and decreases to right.

The relative maximums of the functions are the points where the function makes a downward turn, changing from increasing to decreasing, hence there are two points.

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Answer: the answer is -4

Step-by-step explanation: the reason why the answer is -4 becaue all of the option is in correct.

Answer:  the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

Step-by-step explanation:

a) Let's represent the number of jugs of milk as 'm', the number of loaves of bread as 'b', and the number of pieces of cheese as 'c'. According to the given information:

The total number of items sold today is 224. Therefore, we can write the equation:

m + b + c = 224

The store sold three times as many loaves of bread as jugs of milk. We can write this as:

b = 3m

The store sold four times as many pieces of cheese as loaves of bread. We can write this as:

c = 4b

b) Now, let's solve the equation:

Substituting the value of 'b' from equation (2) into equation (3):

c = 4(3m)

c = 12m

Substituting the values of 'b' and 'c' from equations (2) and (3) into equation (1):

m + 3m + 12m = 224

16m = 224

m = 224 / 16

m = 14

Using the value of 'm' in equation (2):

b = 3m

b = 3(14)

b = 42

Using the value of 'b' in equation (3):

c = 4b

c = 4(42)

c = 168

Answer:

Step-by-step explanation:

a) Let's denote the number of jugs of milk as 'x', the number of loaves of bread as 'y', and the number of pieces of cheese as 'z'.

Based on the given information, we can form two equations:

1) The total number of items sold today is 224:

x + y + z = 224

2) The store sold three times as many loaves of bread as jugs of milk:

y = 3x

3) The store sold four times as many pieces of cheese as loaves of bread:

z = 4y

b) To solve the equations and find the number of jugs of milk, loaves of bread, and pieces of cheese the store sold today, we will substitute equation (2) and equation (3) into equation (1):

x + y + z = 224

x + 3x + 4y = 224

4x + 4y = 224

Now, substitute y = 3x into the equation:

4x + 4(3x) = 224

4x + 12x = 224

16x = 224

Divide both sides by 16:

x = 224 / 16

x = 14

Now substitute the value of x back into equation (2) to find y:

y = 3x

y = 3(14)

y = 42

Finally, substitute the value of y into equation (3) to find z:

z = 4y

z = 4(42)

z = 168

Therefore, the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

The mean of the distribution used in this problem is 3.5.The answer is B. 3.5.

To find the mean of the distribution used in this problem, we need to calculate the expected number of troubles that can be repaired on the same day out of the first five reported. The likelihood of a trouble being repaired on the same day is given as 0.70.

The expected number of troubles repaired on the same day can be calculated by multiplying the probability of each event by the number of trials. In this case, we have five trials (the first five troubles reported) and a probability of 0.70 for each trial.

Expected number of troubles repaired on the same day = Probability of repair on the same day * Number of trials

= 0.70 * 5

= 3.5

This means that, on average, out of the first five troubles reported, we can expect 3.5 of them to be repaired on the same day based on the past data and the given likelihood. So, the correct answer is B. 3.5.

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Answer:

the answer is y=mx+c

Step-by-step explanation:

where the answer is the coefficient of the gradient which is x

The polynomial [tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex] simplifies to [tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18.[/tex]

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is defined as a sum of terms, where each term consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.

The general form of a polynomial is:

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a₀

To simplify the expression[tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex], we need to perform the multiplication and combine like terms.

First, we multiply each term in the first polynomial by each term in the second polynomial:

[tex](x^2 + 3x + 3) * (-2x^2 - x + 6) = x^2 * (-2x^2 - x + 6) + 3x * (-2x^2 - x + 6) + 3 * (-2x^2 - x + 6)[/tex]

Expanding each term, we get:

=[tex](-2x^4 - x^3 + 6x^2) + (-6x^3 - 3x^2 + 18x) + (-6x^2 - 3x + 18)[/tex]

Now, we combine like terms:

=[tex]-2x^4 + (-x^3 - 6x^3) + (6x^2 - 3x^2 - 6x^2) + (18x + 18x - 3x) + 18[/tex]

Simplifying further:

=[tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18[/tex]

The simplified expression in polynomial standard form is:

-2x^4 - 7x^3 - 3x^2 + 33x + 18

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Answer:

16

Step-by-step explanation:

the numbers on the right of the arrow are half the value of the corresponding numbers on the left, then

32 → [tex]\frac{1}{2}[/tex] (32)

32 → 16

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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Answer:

111

Step-by-step explanation:

a² = b² + c² - 2bc cos A

a² = (7√3)² + (√6)² - 2(7√3)(√6) cos 45°

a² = 49 × 3 + 6 - 14√18 × (√2)/2

a² = 153 - 42

a² = 111

a = √111

a = √n = √111

n = 111

The equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Given:Hunger of Harry as a function of time,H(t)H(t) can be modeled by a sinusoidal expression of the form,a⋅cos(b⋅t)+da⋅cos(b⋅t)+d, where Harry wakes up at t=0t=0t=0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs.

Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs.

Therefore, the equation of the form for H(t)H(t) will be,H(t) = A.cos(B.t) + C where, A is the amplitude B is the frequency (number of cycles per unit time)C is the vertical shift (or phase shift)

Thus, the maximum and minimum hunger of Harry can be represented as,When t=0t=0t=0, Harry's hunger is at maximum, i.e., H(0)=30kgH(0)=30kg30, start text, space, k, g, end text.

When t=2t=2t=2, Harry's hunger is at the minimum, i.e., H(2)=15kgH(2)=15kg15, start text, space, k, g, end text.

According to the given formula,

H(t) = a.cos(b.t) + d ------(1)Where a is the amplitude, b is the angular frequency, d is the vertical shift.To find the value of a, subtract the minimum value from the maximum value.a = (Hmax - Hmin)/2= (30 - 15)/2= 15/2 = 7.5To find the value of b, we will use the formula,b = 2π/period = 2π/(time for one cycle)The time for one cycle is (2 - 0) = 2 hours.

As Harry's hunger cycle is a sinusoidal wave, it is periodic over a cycle of 2 hours.

Therefore, the angular frequency,b = 2π/2= π

Therefore, the equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Answer: H(t) = 7.5.cos(π.t) + 22.5.

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Answer:

P(Colin) = 20/38

P(Paul) = 18/38

Step-by-step explanation:

Colin won 20 times out of 38, so the probability that he wins would be 20/38 (or 10/19 simplified).

Paul won 18 times out of 38, so the probability that he wins would be 18/38 (or 9/19 simplified).

Answer:

a) Probability of Colin winning = 10/19

b) Probability of Paul winning = 9/19

Step-by-step explanation:

Total number of matches = 38

Colin won 20,

Paul won the rest so, 38 - 20 = 18

Paul won 18 matches,

From this data, we calculate the probabilities of Colin or Paul winning,

a) Estimate the probability that Colin wins.

Colin won 20 out of 38 matches, so his probability of winning is,

20/38 = 10/19

Probability of Colin winning = 10/19

b) Estimate the probability that Paul wins

Paul won 18 out of 38 matches, so his probability of winning is,

18/38 = 9/19

Probability of Paul winning = 9/19

Answer:    -8 ≥ x

Step-by-step explanation:

Let x be the number, we set up an inequality:

-183 ≥ 9 + 24x    [we use ≥ to present "at least"]

-192 ≥ 24x

  -8 ≥ x

Answer:

BC = 24 (D)

Step-by-step explanation:

Special Right Triangles (30-60-90 triangle)

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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By conducting a statistical test with the provided data and using a significance level of 0.05 and a critical value of 0.811, the educator can determine whether the number of absences significantly affects the final grade of the students.

To analyze the relationship between the number of absences and the final grade of students, an educator collected data from a sample. The obtained data reveals that for 10 absences, the corresponding final grade was 70. In order to determine whether the number of absences significantly impacts the final grade, a statistical test is needed.

The information provided, "Test at α = 0.05, XCV = 0.811," suggests that the educator is referring to a significance level (α) of 0.05 and the critical value (XCV) associated with this level is 0.811.

To conduct a hypothesis test, the educator needs to set up the null (H0) and alternative (Ha) hypotheses. In this case, the null hypothesis would assume that the number of absences does not have a significant effect on the final grade. The alternative hypothesis would assume that the number of absences does have a significant effect on the final grade.

Using the obtained data, the educator would perform the statistical test, such as a correlation analysis or a regression analysis, to determine the strength and significance of the relationship between absences and final grade.

If the test statistic (such as the correlation coefficient or regression coefficient) exceeds the critical value, the null hypothesis would be rejected, suggesting that the number of absences does have a significant impact on the final grade.

The educator can then interpret the results, considering factors such as the direction and strength of the relationship. Additionally, they may explore other variables or factors that could be influencing the final grade and further refine their analysis.

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Answer:h equals 12

Step-by-step explanation:

Answer: c. known

Step-by-step explanation:

In random sampling, the probability of selecting an item from the population is known. This probability can be calculated based on the sampling method and the characteristics of the population being sampled. Random sampling ensures that each item in the population has an equal chance of being selected, making the probability of selection known and calculable.

Answer:

Step-by-step explanation:

To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:

a) g(0)

To find g(0), substitute x = 0 into the function:

g(0) = 2(0)^2 - 2(0) + 9

g(0) = 0 - 0 + 9

g(0) = 9

b) g(-1)

To find g(-1), substitute x = -1 into the function:

g(-1) = 2(-1)^2 - 2(-1) + 9

g(-1) = 2(1) + 2 + 9

g(-1) = 2 + 2 + 9

g(-1) = 13

c) g(2)

To find g(2), substitute x = 2 into the function:

g(2) = 2(2)^2 - 2(2) + 9

g(2) = 2(4) - 4 + 9

g(2) = 8 - 4 + 9

g(2) = 13

d) g(-x)

To find g(-x), substitute x = -x into the function:

g(-x) = 2(-x)^2 - 2(-x) + 9

g(-x) = 2x^2 + 2x + 9

e) g(1 - t)

To find g(1 - t), substitute x = 1 - t into the function:

g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9

g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9

g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9

g(1 - t) = 2t^2 - 2t + 9

Therefore:

a) g(0) = 9

b) g(-1) = 13

c) g(2) = 13

d) g(-x) = 2x^2 + 2x + 9

e) g(1 - t) = 2t^2 - 2t + 9

Answer:

Step-by-step explanation:

[tex]P(\text{not vanilla})=1-\frac{3}{22}=\frac{19}{22}[/tex]

Odds are 19 to 3.

Answer:

Step-by-step explanation:

To find the time it takes for the turtle to reach the pond, we can use the formula:

Time = Distance / Speed

Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:

Time = (5/6) / (1/12)

To simplify this, we can multiply the numerator by the reciprocal of the denominator:

Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10

Therefore, it will take the turtle 10 hours to reach the pond.

The linear equation from the given table is expressed as:

y =  -1500x + 8350

The general form for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The formula for the equation of a line through two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

We will take the two coordinates (1, 6850) and (2, 5350)

Thus:

(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)

(y - 6850)/(x - 1) = -1500

y - 6850 = -1500x + 1500

y = -1500x + 1500 + 6850

y =  -1500x + 8350

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Answer:

A. 16% of scores are at his/her score or below

Step-by-step explanation:

When a student's score is at the 16th percentile, it means that their score is equal to or better than 16% of the scores in the population. In other words, 16% of the scores are at their score or below.

Answer:

acute triangle

Step-by-step explanation:

for the given sides to form a triangle

the sum of any 2 sides must be greater than the third side

given 56 , 90 , 100

56 + 90 = 146 > 100

56 + 100 = 156 > 90

90 + 100 = 190 > 56

the condition is met so the 3 lengths will form a triangle.

let a = 56 , b = 90 and c = 100 , where c represents the longest of the 3 sides , then

• if a² + b² = c² , then triangle is right

• if a² + b² > c² , then triangle is acute

• if a² + b² < c² , then triangle is obtuse

a² + b² = 56² + 90² = 3136 + 8100 = 11,236

c² = 100² = 10, 000

since a² + b² > c² , then triangle is acute

Answer:

this question is incomplete