Lena, Alan, and Bill sent a total of 104 text messages over their cell phones during the weekend. Lena sent 8 fewer messages than Alan. Bill sent 2 times as many messages as Lena. How many messages did they each send?

To translate the function y = |x| one unit value downward, we need to subtract 1 from the function: y = |x| - 1.

The function y = |x| is a V-shaped graph that passes through the origin and has a slope of 1 on both sides. It represents the absolute value of x, which means that the function always returns a positive value regardless of whether x is positive or negative.

To translate the function one unit downward, we need to subtract 1 from the function. This means that for any given value of x, the function will return the absolute value of x minus 1. For example, if x = 2, then y = |2| - 1 = 1. If x = -2, then y = |-2| - 1 = 1.

The resulting graph of y = |x| - 1 is still a V-shaped graph, but it is shifted down by one unit compared to the graph of y = |x|.

Thus, the slope of the graph remains the same on both sides, but the minimum value of y is now -1 instead of 0.

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Based on the information, we can answer the questions as follows:

An experimental study is a research design in which the researcher manipulates one or more independent variables and measures the effects of those manipulations on one or more dependent variables, while controlling for other potentially relevant factors (known as extraneous variables).

Therefore, he goal of an experimental study is to establish a cause-and-effect relationship between the independent variable(s) and the dependent variable(s).

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The only number that is a factor of 63 and 6363 is option B: 3,  while the other options are not factors

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

To determine which of the given numbers is a factor of 63 or 6363, we need to check if they divide the given numbers without leaving any remainder.

Option A: 6

63 ÷ 6 = 10 remainder 3

6363 ÷ 6 = 1060 remainder 3

Since both calculations leave a remainder of 3, 6 is not a factor of 63 or 6363.

Option B: 3

63 ÷ 3 = 21

6363 ÷ 3 = 2121

Since both calculations give a whole number without any remainder, 3 is a factor of 63 and 6363.

Option C: 8

63 ÷ 8 = 7 remainder 7

6363 ÷ 8 = 795 remainder 3

Since both calculations leave a remainder, 8 is not a factor of 63 or 6363.

Option D: 2

63 ÷ 2 = 31.5

6363 ÷ 2 = 3181.5

Since both calculations give a non-integer result, 2 is not a factor of 63 or 6363.

Therefore, the only number that is a factor of 63 and 6363 is option B: 3,  while the other options are not factors

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The correct graph for the given data is given by option The bar graph x axis labeled sport and the y axis labeled number of students, with each having value as basketball -17, baseball-12, soccer - 27, and tennis - 44.

Because the data shows discrete categories (sports) and their related frequencies, the correct graph is a bar graph (number of students).

The x-axis is to be named "Sports" to represent the various sports (Basketball, Baseball, Soccer, and Tennis), and the y-axis has to be labelled "Number of Students" to reflect the frequency. The graph's bars will show the frequency of each sport, with the heights of the bars giving the number of students who identified each sport as their favourite. The right values for the bars should be based on the data provided:

[tex]Basketball: 17\\Baseball: 12\\Soccer: 27\\Tennis: 44[/tex]

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The number line that represents the solution to the inequality 3x-8≥7 is shown on the attached image.

The inequality: 3x - 8 ≥ 7

Add 8 to both sides

3x ≥ 7 + 8

Add 7 and 8 to get 15

3x ≥ 15

Divide both sides by 3

3x/3 ≥ 15/3

x ≥ 5

An inequality is a mathematical statement that compares two values or expressions, indicating whether they are equal or not. Unlike equations, which are true only if the two sides are equal, inequalities may be true for different values on either side of the inequality sign.

Inequalities are often represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

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The domain of the function plotted is

In mathematics, the domain of a function is the set of all possible values of the input (independent variable) for which the function is defined.

So we can say that, it is the set of all possible values that we can substitute into the function and get a valid output (dependent variable).

In the graph, watching the x axis which is the input variables we can see that the domain is all real numbers from -4 to 4

In general, the domain of a function depends on the specific form of the function and any restrictions or conditions that may apply to the input values.

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Answer: Without additional information about the study and the definition of "high level of satisfaction," we cannot determine the probability that a randomly chosen customer did not have a high level of satisfaction with the company.

The probability would depend on the specific criteria used to define a high level of satisfaction, as well as the distribution of satisfaction levels among the customers in the study.

If we have access to this information, we could use it to calculate the probability that a randomly chosen customer did not have a high level of satisfaction using the appropriate formulas or statistical techniques.

Step-by-step explanation:

The radius of the base of the cone-shaped block is approximately 10.69 inches.

We can use the formula for the volume of a cone to find the radius of its base. The volume of a cone is given by the formula  :

V = (1/3)πr^2h

Where

We know that the volume of the cone-shaped block is 125 cubic inches, and we know the height is the same for all blocks. So we can solve for the radius:

125 = (1/3)πr^2h

125 = (1/3)πr^2h

375 = πr^2h

r^2 = 375/π

r ≈ 10.69

So we can conclude that the radius of the base of the cone-shaped block is approximately 10.69 inches.

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Perry como fans fifty-six percent of respondents to an online poll said that they were perry como fans. if 982 randomly selected people responded to this poll.

By use the sample proportion to estimate the true proportion of all local residents who are Perry Como fans.

Let p be the true proportion of all local residents who are Perry Como fans. Then, the sample proportion is 0.56 and the sample size is n = 982.

We construct a 95% confidence interval for p by using the formula

Sample proportion ± z*standard error

Where z is the critical value from the standard normal distribution for a 95% confidence level, which is 1.96. The standard error is the estimated standard deviation of the sample proportion which is defined as

[tex]\sqrt{p*(1-p)/n} \\}[/tex]

By putting the values we get

Standard error = [tex]\sqrt{0.56*(1-0.56)/982)[/tex] = 0.018.

95% confidence interval = 0.56 ± 1.96*0.018 = (0.525, 0.595).

Hence, we can say with 95% confidence that the true proportion of all local residents who are Perry Como fans is between 0.525 and 0.595.

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Answer:

[tex]15 + 45 = 3(5 + 15)[/tex]

Hence,The equation that models the height of the roller coaster is  [tex]x^{2} +y^{2}=900[/tex]. and solution of y =[tex]\sqrt{(900-x^{2})}[/tex].

A roller coaster, or roller coaster, is a type of amusement ride that employs a form of elevated railroad track designed with tight turns, steep slopes, and sometimes inversions. Passengers ride along the track in open cars, and the rides are often found in amusement parks and theme parks around the world.

We have given that ,

the Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.

we know that equation of circle ,

[tex]x^{2} +y^{2}=r^{2}[/tex]

Where r is the radius

From given we can say that the radius =30

since the radius is 30 ft

[tex]x^{2} +y^{2}=30^{2}\\x^{2} +y^{2}=900[/tex]

so, the equation that models the height of the roller coaster. [tex]x^{2} +y^{2}=900[/tex].

We have to find the equation that can be represent the height of the roller coaster so find the value of y

[tex]x^{2} +y^{2}=r^{2}[/tex]

⇒[tex]y^{2}=r^{2}-x^{2}[/tex]

⇒[tex]y^{2}=30^{2}-x^{2}[/tex]

⇒[tex]y^{2}=900-x^{2}[/tex]

⇒y =±[tex]\sqrt{(900-x^{2})}[/tex]

⇒y =[tex]\sqrt{(900-x^{2})}[/tex]   ∵according to question choose positive sign only

Therefore the models the height of the roller coaster y =[tex]\sqrt{(900-x^{2})}[/tex].

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The measurement of the angle labeled (3x)° include the following: 120°.

In Mathematics and Geometry, corresponding angles postulate simply refers to a theorem which states that corresponding angles are always congruent (equal) if the transversal intersects two parallel lines.

This ultimately implies that, the corresponding angles would always be congruent (equal) if a transversal intersects two (2) parallel lines.

60 + y = 180

y = 180 - 60

y = 120°

By applying corresponding angles postulate to both lines a, b, and w, we can reasonably infer and logically deduce that the following angles are congruent:

3x = 120°

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The account value after forty (40) years is approximately $2,789,525.

We can use the formula for future value of an annuity to solve this problem:

FV = PMT * ((1 + r)^n - 1) / r

where FV is the future value, PMT is the annual deposit amount, r is the annual interest rate, and n is the number of periods (years in this case).

For the first year, the deposit amount is $3,000, so:

FV1 = 3000 * (1 + 0.0835)^40 = $65,470.22

For the subsequent years, the deposit amount increases by $300, so:

PMT = 3000 + 300 + 300 + ... = 3000 + 300 * 39 = $15,300

Using this value for PMT, we can calculate the future value for the remaining 39 years:

FV2 = 15300 * ((1 + 0.0835)^39 - 1) / 0.0835 = $2,724,054.54

Adding the two future values together, we get the total account value after forty years:

FV = FV1 + FV2 = $2,789,524.76

Therefore, the account value after forty years is approximately $2,789,525.

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Answer:b

Step-by-step explanation:

Answer:

b and c

Step-by-step explanation:

b 5(7+6s—9t)

35+30s—45

c 10×(3.5+3s—4.5t)

10×3.5 +10×3s—10×4.5t

35+30s—45t

The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

What is meant by days?

Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.

Explain whole numbers

Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.

According to the given information

The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).

In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:

S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)

    ≈ 1200

So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

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A method of assigning probabilities based on historical data is called the Empirical Probability method.

Empirical probability refers to the probability of an event based on observed data or past experience.

It is also known as experimental probability because it is determined through experimentation or observation.

This approach involves analyzing past events and their outcomes to calculate the probability of a particular event happening in the future.

To calculate empirical probability, you can use the formula:
Empirical Probability = (Number of successful outcomes) / (Total number of outcomes)
In this method, you collect and analyze historical data to make predictions about future events.

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The answer depends on the rank of A.

If the rank of A is less than 4, then the dimension of its null space is greater than or equal to 4-rank(A).

If the rank of A is 4, then the dimension of its null space is 0.

The dimension of the null space of a matrix A is given by the number of linearly independent vectors that satisfy the equation A x = 0,

where x is a column vector.

Since A is a 6x4 matrix, the equation A x = 0 represents a homogeneous system of 6 linear equations in 4 unknowns.

The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns of the matrix. Therefore, we have:

rank(A) + dim(null(A)) = 4

The rank of A is at most 4, since there are only 4 columns.

If the rank of A is 4, then the dimension of its null space is 0, because there are no linearly independent vectors that satisfy A x = 0. On the other hand, if the rank of A is less than 4, then the dimension of its null space is at least 4-rank(A).

Therefore, the smallest possible dimension of null(A) is:

dim(null(A)) = 4 - rank(A).

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The smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

To determine the smallest possible dimension of the null space (nul A) of a 6x4 matrix A, we need to consider the rank-nullity theorem, which states:

dim(A) = rank(A) + dim(nul A)

Here, dim(A) represents the dimension of the matrix A, rank(A) represents the rank of the matrix A, and dim(nul A) represents the dimension of the null space of A.

For a 6x4 matrix A, the dim(A) is 4 since there are 4 columns. The rank(A) represents the number of linearly independent columns, and it can be at most 4 since there are 4 columns.

To find the smallest possible dimension of the null space, we need to maximize the rank(A). In this case, the maximum possible rank(A) is 4. Now, using the rank-nullity theorem:

4 = 4 + dim(nul A)

Solving for dim(nul A), we get:

dim(nul A) = 4 - 4
dim(nul A) = 0

Therefore, the smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

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An adiabatic process is one in which the heat transered between a system and its surroundings is equal to zero( q = 0 ). So, option(e) right one.

In thermodynamics, the adiabatic process is a process in which there is no heat or air exchange between the temperature and the environment. It is different from the isothermal heat flow process. Some important properties are :

Hence, option(e) is right answer.

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The appendix table the point estimate of the difference between the two population means is 2

The difference between the two population means, we need to find the standard error of the difference and use the t-distribution with (n1 + n2 - 2) degrees of freedom. The formula for the standard error of the difference is:

SE = sqrt[ (s1 / n1) + (s2 / n2) ]

Substituting the given values, we get:

SE = sqrt[ (2.4 / 50) + (3 / 35) ] = 0.617

Using a t-distribution with 83 degrees of freedom (50 + 35 - 2), and a 90% confidence level, we find the t-value to be 1.66 (from the t-table or calculator). Therefore, the 90% confidence interval is:

x1 - x2 ± t(α/2) * SE

= 2 ± 1.66 * 0.617

= 0.98 to 3.02

So, we can say with 90% confidence that the true difference between the two population means lies between 0.98 and 3.02.

To calculate the 95% confidence interval:

x1 - x2 ± t(α/2) * SE

= 2 ± 2.00 * 0.617

= 0.79 to 3.21

So, we can say with 95% confidence that the true difference between the two population means lies between 0.79 and 3.21.

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The interval for which the ball's height is increasing on the graph, would be 0 seconds to 1.5 seconds.

The interval for which the ball's height is increasing is when the slope of the graph is positive, or when the height is increasing with respect to time.

Looking at the graph, we can see that the ball starts at a height of 0 meters and reaches a peak of 11.025 meters at 1.5 seconds. After 1.5 seconds, the ball begins to fall back to the ground.

Therefore, the interval for which the ball's height is increasing is from 0 seconds to 1.5 seconds. During this interval, the height of the ball is increasing as it travels upwards, reaching its peak at 1.5 seconds. After 1.5 seconds, the height of the ball starts decreasing as it falls back down to the ground.

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After solving the given angles we can conclude that ∠4 is (D) 140° respectively.

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry.

Two rays can form angles in the plane where they are positioned.

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

Acute, obtuse, right, straight, reflex and full rotation are examples of basic angles.

So, according to the given image, we know that:

∠ 1 + ∠ 2 = 180

Then,

(3x + 20) + x = 180

4x + 20 = 180

4x = 180 - 20

4x = 160

x = 160 / 4

x = 40

We got that:

∠ 1 = ∠ 4

∠ 2 = ∠ 3

Simply substitute for x and solve if ∠1 = ∠4:

3x + 20 = 3(40) + 20 = 120 + 20 = 140

Therefore, after solving the given angles we can conclude that ∠4 is (D) 140° respectively.

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Jerel runs 4 km on the sixth day.

Let's call the distance Jerel runs on the sixth day "x". We know that he runs 4.2 km each day for the first 6 days, so the total distance he runs in those 6 days is:

Total distance = 4.2 km/day x 6 days = 25.2 km

We also know that the total distance Jerel runs is 25 km, so we can set up an equation to solve for "x":

4.2 km/day x 5 days + x = 25 km

Simplifying the equation, we get:

21 km + x = 25 km

Subtracting 21 km from both sides, we get:

x = 25 km - 21 km

x = 4 km

Therefore, Jerel runs 4 km on the sixth day.

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The answer choices which fit into the descriptions as given in the task content are; Squares and Rhombus.

It follows from the task content that the given quadrilateral is such that; FG || HI, GH || IF and FH = GI. However, since the diagonals are perpendicular.

Consequently, it can be inferred that the diagonals of squares and Rhombuses are perpendicular. On this note, the shapes which best align with the given descriptions are; Square and Rhombus.

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Answer:

-60

Step-by-step explanation:

Farm Joe used [tex]7\frac{6}{15}[/tex] kg of soil in this month.

The total weight of soil that Farm Joe ordered was:

3 bags x 4 2/5 kg/bag = 12 6/15 kg = 12 2/5 kg

The weight of the first bag used was 4 2/5 kg.

The weight of the second bag remaining is 2 3/4 kg.

The weight of the third bag remaining is 7/8 kg.

The total weight of soil used in this month can be found by subtracting the weight of the second and third bags remaining from the total weight of soil ordered:

12 2/5 kg - 2 3/4 kg - 7/8 kg

Converting all fractions to fifteenths:

12 8/15 kg - 5 1/15 kg - 1/15 kg = 7 6/15 kg

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Answer:

Step-by-step explanation: Multiplication first 7x1 = 7, Take 7 and divide it by 10 which gives you 0.7, Do the same but for the other 2 questions,

(9x1/100 = 0.09)

(9x1/1000 = 0.009)

(7x1/10 = 0.7)

Now take the answers and add them up

0.09 + 0.009 + 0.7 = 0.799

Answer: 0.799

The values of x and y for the tangent segments to the circle A are: 4 and 8.899 respectively.

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

KJ = K L

6x - 3 = 5x + 1

6x - 5x = 1 + 3 {collect like terms}

x = 4

IJ = IH = 11

y² - 10 = 4y + 2

y² - 4y - 2 - 10 = 0

y² - 4y - 8 = 0 {quadratic equation}

using the quadratic formula

y = 8.899 or y = -0.898

Therefore, the values of x and y for the tangent segments to the circle A are: 4 and 8.899 respectively.

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The probability of hitting the black circle inside the target is approximately 0.0314.

The probability of hitting the white portion of the target is approximately 0.686.

Part A:

The black circle has a diameter of 2 units, which means it has a radius of 1 unit. The area of the circle is πr^2, which is π(1)^2 or π square units. The area of the white square is 10 x 10 or 100 square units.

The probability of hitting the black circle inside the target is the ratio of the area of the circle to the area of the square, which is π/100 or approximately 0.0314. This probability is closer to 0 because the circle is much smaller than the square, and the likelihood of hitting the exact center of the circle is low.

Part B:

The white portion of the target is the area of the square minus the area of the black circle, which is 100 - π square units.

The probability of hitting the white portion of the target is the ratio of the area of the white portion to the area of the square, which is (100-π)/100 or approximately 0.686.

This probability is closer to 1 because the white portion of the target is much larger than the black circle, and there are many possible areas of the square that could be hit.

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The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The volume of a cone is a third of the volume of a cylinder, hence:

V = πr²h/3.

For both cases, the height variable h has an exponent of one, hence:

If we had doubled the radius for example, the volume would be multiplied by 2² = 4, as the radius is squared.

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Answer to these fraction is 31/151

Describe fraction.

Any numerical value that is not a whole number is referred to as a fraction. It symbolizes a portion of something or several portions of something. The numerator and the denominator are the two components of a fraction. The denominator indicates how many equally sized pieces make up a whole, whereas the numerator indicates how many equally sized parts are picked from the whole or collection.

To divide a fraction, all you need to do is flip its numerator and denominator, multiply the outcome by the other fraction, and simplify1.

In light of this, we have:

SUM:

(13/5) + (-12/7) = (13× 7 + -12 ×5) / (5 ×7)

= (91 - 60) / 35 = 31/35

DIFFERENCE:

(13/5) - (-12/7) = (13× 7 - -12× 5) / (5× 7)

= (91 + 60) / 35 = 151/35

Dividing these two fractions:

(31/35) ÷ (151/35) = (31/35)×(35/151) = 31/151

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