What is the length of AB

Following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.

In mathematics, an integral assigns numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data.

Integration is the action of locating integrals.

So, the number of automobiles that cross an intersection each hour is:

r(t) = 400 + 800t - 120t²

Integration should be carried out to establish the number of cars traveling through the intersection between 6 am and 8 am.

[tex]\begin{aligned}\int_{t_1}^{t_2} r d t & =\int_0^2 400+800 t-120 t^2 d t \\& =\left[400 t+400 t^2-40 t^3\right]_0^2 \\& =400 \times 2+400 \times 2^2-40 \times 2^3 \\& =800+1600-320 \\& =2080\end{aligned}[/tex]

Therefore, following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.

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Correct question:
The traffic flow rate (cars per hour) across an intersection is r ( t ) = 400 + 800 t − 120 t 2 , where t is in hours, and t =0 is 6am. How many cars pass through the intersection between 6 am and 8 am?

The expected difference under null hypothesis can be understood by the following :

The required null and alternate hypothesis will be

Null hypothesis :  H0 : μ=μ0

Alternate Hypothesis: H1 : μ<μ0

To determine whether there is a difference in the means of two populations, the z test formula compares the z statistic to the z critical value.

The z critical value in hypothesis testing divides the distribution graph into acceptance and rejection regions. The null hypothesis can be rejected if the test statistic falls within the rejection region; otherwise, it cannot be rejected.

The z test formula  to set up the required hypothesis tests for a one sample and a two-sample z test is

z = (( x−μ) /σ/√n  )x

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Answer:

Below

Step-by-step explanation:

.046 is lost each year meaning  (1 - .046) remains

A(t) = 300 ( 1 - .046)^t        will show milligrams remaining after 't' years (where t is the years since 2004)

The Rate of Sales Tax in Percentage is 1.25%

What is Percentage?

Percentages: The percentage is one of the most used methods to portray statistics. Percentage simply means "per hundred," and the sign for percentage is %. One percent (or 1%) is one hundredth of a total or whole number and is computed by dividing the whole or entire number by 100.

Solution:

Cost Price of the Cookie Jar is given as $1.60

And, Selling Price is $1.62 including Sales Tax

We need to calculate the Rate of Sales Tax

So, the amount of Sales Tax is 0.02$

Percentage is 0.02/1.6 * 100 = 1.25%

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The discounted price of an item did the price increased after the weekend by a fraction of 1/5.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. One-fifth is 20 percent of the total five parts of a number, and thus, the price increased by 1/5th after the weekend.

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Answer:

q = 50

r = 75

s = 115

t = 30

Step-by-step explanation:

a.)The 95% Confidence interval for the average difference between the reading and writing scores of all students is 0.545 ± 1.232.

b.) Since independent random samples are chosen from a population that is roughly typical

The number of degrees of freedom with an unknown standard deviation is n-2.

c.)The null hypothesis could not be rejected because the aforementioned interval contains zero. 

Using a confidence interval does not show conclusive proof that there is a genuine difference in the average results .

Therefore there is no real  difference in the average scores.

Z = X  +- 1.96 ( SD/ √n  )

= 0.545 ± 1.96 × 8.887

√2000.545 plus or minus 1.96 times 8.887 over the square root of 200

= 0.545 ± 1.232

Out of 100 samples, the population mean would range between -0.687 and 1.777 on average in 95 of them.

explanation for part b,

n = 7, CL = 90%

df= 7-2=5t*=1.476(one tail),

2.015(both tails)

n = 26, CL = 98%

df= 26-2=23t*=2.177(right tail),

2.5(both tail)

n = 28, CL = 95%

df=28-2=26t*=1.706(one tail),

2.056(both tail)

n = 11, CL = 99%

df= 11-2=9t*=2.821 (one tail),

3.250(both tail)

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The value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6

What is the interquartile range (IQR) of the data?

The interquartile range (IQR) of the data is the middle half of the data, which contains 2nd and 3rd quartiles.

Interquartile range is the difference of third quartile and first quartile.

IQR = Q₃ - Q₁

According to the given question:

In the dot plot below, the data is given as,

0 2 4 6 8 10 12

The first quartile is the medium of the lower half, while the third quartile is the medium of the upper half. For the above data,

Q1 = 3

Q3 = 9

Thus, Interquartile range is,

IQR = Q₃ - Q₁

IQR = 9 - 3

IQR = 6

Hence, the value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6

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Answer:

The following statements are true:

A) The equation |-x - 4| = 8 will have two solutions.

D) The equation |2x - 10| = -20 will have two solutions.

E) The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions.

The other statements are not true. The equation 3.4|0.5x - 42.1| = -20.6 will not have one solution, as the absolute value of a number cannot be negative. The equation |1/2x - 3/4| = 0 will not have no solutions, as the absolute value of a number cannot be zero. The equation |1/8x - 1| = 5 will not have infinitely many solutions, as the absolute value of a number cannot be negative.

Step-by-step explanation:

The equation of the regression of grades on scores is y = 0.003x + 1.645

The mean of the sat scores = 485

The standard deviation = 85

The average college gpa = 3.1

The standard deviation = 0.4

The correlation between sat scores and college grades = 0.71

The regression equation is

y = mx + b

The value of m = (0.71) × (0.4/85)

= 0.003

Substitute the values in the regression equation and find the value of b

3.1 = 0.003×485 + b

3.1 = 1.455 + b

b = 3.1 - 1.455

b = 1.645

The equation is

y = 0.003x + 1.645

Therefore, the regression equation is y = 0.003x + 1.645

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The inequality to represent the problem is x + 1.25y ≥ 2000 and it's graph is attached below

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in mathematics. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).

Let;

a) The inequality to represent the situation can be expressed as

1x + 1.25y ≥ 2000

This is further expressed as;

x + 1.25y ≥ 2000

b) The graph of the inequality x + 1.25y ≥ 2000 is attached below.

c) The possible solutions are at (2000, 0) and (0, 1600)

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The time taken by the jet to reach the earth form sun is 3 months

The correct option is option A)

What is speed?

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

We are given that

Light travels at the speed of 3,00,000 km per second. Light from the sun reaches us in 8 minutes

We first find the distance between sun and earth

to do that we multiply speed of light and time taken by light to reach earth

D = 300000*8

D= 2400000km

Now we are given the speed of the jet which is 1000km/hr

We have to find the time taken by the jet to reach the earth

To do that we divide the distance by speed we get

t = 2400000/1000

t =2400 hr.

3 months

The time taken by the jet to reach the earth form sun is 3 months

The correct option is option A)

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Answer:

p=500

Step-by-step explanation:

18/100=90/p

First, set up equation

90x100=18xp

9000=18p

9000/18=18p/18

500=p

Answer:

[tex]p = 500[/tex]

Step-by-step explanation:

Use the cross-multiplication method. Multiply 18 with p, and 90 with 100, respectively:

[tex]\frac{18}{100} = \frac{90}{p} ; \\ 18p = 90 * 100\\ 18p = 9000[/tex]

Isolate the variable, p. Note the equal sign, what you do to one side, you do to the other. Divide 18 from both sides of the equation:

[tex]\frac{(18p)}{18} = \frac{(9000)}{18} \\p = \frac{9000}{18} \\p = 500[/tex]

[tex]p = 500[/tex] is your answer.

~

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The area of the triangle formed by the birdbath, bird feeder and the birdhouse is 15 squared units

Given: the birdbath is at (2,2), the bird feeder is at (8,2), and the birdhouse is at (5,7)

(Consider the image attached)

The distance between the points can be calculated using the formula:

d=√((x2 – x1)² + (y2 – y1)²)

birdbath (5,7) and birdhouse (2,2)

d=√((2 – 5)² + (2 – 7)²) = √34

bird feeder (8, 2) and birdhouse (2,2)

d=√((2 – 8)² + (2 – 2)²) = 6

birdbath (5,7) and bird feeder (8,2)

d=√((8 – 5)² + (2 – 7)²) = √34

The height of the triangle is:

h = √((√34)²-3²) = 5

Area of triangle = 1/2 × base × h

Area of triangle = 1/2 × 6 × 5 = 15 squared units

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A line plot would be the best data display to highlight every height.

A line plot, also known as a dot plot, is a type of graph that displays data as a series of dots on a number line. Each dot represents a single data point, and the dots are placed above the corresponding value on the number line.

Line plots are useful for displaying small data sets because they provide a simple visual representation of the data. They can quickly show the range of values in the data set, as well as any outliers or clusters of data points. Line plots are commonly used in elementary and middle school classrooms to teach basic data analysis and graphing skills. They are also used in scientific research and statistical analysis to visualize small data sets and identify patterns in the data.

A line plot, also known as a dot plot, displays the data as points on a number line. Each data point is represented by a dot, making it easy to see every height in the data set. Here is an example of a line plot for the given data:

A display that will highlight every height would be a line plot, which would show each individual height as a dot along a number line.

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Answer:

x=1,13

Step-by-step explanation:

(x – 7)^2 = 36

To solve for x take the square root of each side

sqrt((x – 7)^2) = sqrt(36)

x-7 = ±6

Splitting into two equations

x-7 = 6    x-7 = -6

Add 7 to all sides

x-7+7 = 6+7    x-7+7 = -6+7

x=13                          x=1

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(x - 7)^2 = 36}[/tex]

[tex]\mathsf{(x - 7)(x - 7) = 36}[/tex]

[tex]\mathsf{x^2 - 14x + 49 = 36}[/tex]

[tex]\text{SUBTRACT 36 to BOTH SIDES}[/tex]

[tex]\mathsf{x^2 - 14x + 49 + 49 = 36 + 49}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x^2 - 14x + 13 = 36 + 49}[/tex]

[tex]\mathsf{x^2 - 14x + 13 = 0}[/tex]

[tex]\text{FACTOR the LEFT SIDE of your equation}[/tex]

[tex]\mathsf{(x - 1)(x - 13) = 0}[/tex]

[tex]\text{SET the FACTORS to EQUAL to 0}[/tex]

[tex]\mathsf{Equation\ \#1.)\ \rightarrow x - 1 = 0}[/tex]

[tex]\mathsf{Equation\ \#2.)\ \rightarrow x - 13 = 0}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x = 1 \ or\ x = 13}[/tex]

[tex]\huge\text{Thus, your answer should be: } \boxed{\mathsf{x = 1 \ or\ x = 13}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The probability that the resulting integer is divisible by 8 is 1/6

According to the question,

Nancy Rolled a six-sided die twice to generate two-digit integers

Total number of outcome by rolling a die = {1 , 2 , 3 , 4 ,5 ,6 }

If you roll twice then total number of outcomes becomes = 6 × 6

=> 36

We have to find  the probability that the resulting integer is divisible by 8

Number of two - digit integer divisible by 8 = 16 , 24 , 32 , 48 , 56 , 64

that is 6  

So, Probability = Number of favorable outcomes / total number of outcomes

=> 6 / 36

=> 1/6 is required probability

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20 people need to be in a group in order for them to save $500.

If there are 15 people or more, people will save $25 on each ticket.

In order to save a total of $500, the number of people who are needed is:

= Amount to be saved / Amount to be saved per ticket

= 500 / 25

= 20 people

In conclusion, if a group of 20 people came, they would save $500.

If a gardner plants 90 seedlings. the number of seedlings in each row is 3 more than twice the number rows then 43.5 number of rows are planted by the gardner.

Two or more expressions with an Equal sign is called as Equation.

Given,

Gardner plants 90 seedlings

The number of seedlings in each row is 3 more than twice the number rows.

We need to find the number of rows.

Let r be the number of rows

2r+3=90

Subtract 3 from both sides

2r=87

Divide both sides by 2

r=43.5

Hence, 43.5 number of rows are planted by the gardner.

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By solving a linear equation we will see that the value of x is 10.

Remember that for any triangle, the sum of all internal angles is always equal to 180°.

Here only look at triangle BCD, we know that:

m∠DBC = m∠ABC = 3x

m∠BCD = m∠ACB + m∠ABD = 2x + 65°

m∠ADC = 65°

Now we can write the linear equation as:

3x + 2x + 65° + 65° = 180°

5x + 130° = 180°

5x = 180° - 130°

5x = 50°

x = 50°/5 = 10°

The value of x is 10.

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Answer:

100 is the answer

Step-by-step explanation:

The correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."

The relationship between two terms on either side of an equal sign is easily demonstrated using a simple equation.

Additionally, one or more of the four arithmetic operations that simple equations do include addition, fundamental arithmetic, multiplication, and division.

The three possible forms of the equation system are point-slope form, standard form, and slope-intercept form.

So, given equations:

y = 1/2 * x - 3

y = - 1/2 * x - 3

As we are aware, a line's slope-intercept form is:

y = m x + c  

Therefore, it is clear from equations 1 and 2 that:

m1 = 1/2 and c1 = -3

m2 = -1/2 and c2 = -3

Therefore, the correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."

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Complete question:
A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?

a. They have the same slope but different y-intercepts, so they have no solution.

b/. They have the same slope but different y-intercepts, so they have one solution.

c. They have different slopes but the same y-intercept, so they have no solution.

d. They have different slopes but the same y-intercept, so they have one solution.

The sum of the area of the rectangle has an area of 5x + 22 ft²rectangle b has an area of 8x - 2  ft² is  13x + 20  ft².

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

The area of a rectangle, A = 5x+22 ft²,

The area of a rectangle, B = 8x-2 ft²,

Calculate the sum of the areas as shown below,

A + B = 5x + 22 + 8x - 2

A + B = 13x + 20  ft²

Therefore, the sum of the area of the rectangle has an area of 5x + 22 ft²rectangle b has an area of 8x - 2  ft² is  13x + 20  ft².

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The difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.

Here, we are given that 13.4% of the population in the US lived in the West in 1950 and 22.5% in 2000.

Thus, the difference in percentage = 22.5 - 13.4 = 9.1%

We observe that the difference is large, this means that the difference in percentages is practically significant.

Now, to determine whether the difference is statistically significant it is appropriate to conduct a two-sample z-test and it is only appropriate to conduct the test of significance when the samples are simple random samples.

In this case, the samples are not simple random samples, because the data given contains information on all individuals in the population. Moreover, it is not appropriate to determine whether the difference in percentages is statistically significant as the samples are not probability samples.

Thus, the difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.

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The perpendicular bisector of the line is option c)

The bisector of the angle YXZ is option B)

The perpendicular from point Z to the line XY is option G)

What is perpendicular bisector?

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

We are asked to find the perpendicular bisector on the line XY

Now this means a segment dividing segment XY in two equal parts and intersecting XY at right angle

Hence This description match with option C)

Hence The perpendicular bisector of the line is option c)

Similarly,

The bisector of Angle YXZ will be the line which divides the angle in two equal parts

This description matches with option B)

Hence the correct option is option B)

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Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The area of a shape is the space enclosed within the perimeter or the boundary of the given shape.

Here, μ = 100, σ = 15 and x = 125. We need to compute P(X >= 125). The corresponding z-value is calculated using Central Limit Theorem.

z = (x - μ)/σ

z = (125 - 100)/15 = 1.67

z = 1.67

Therefore,

P(X >= 125) = P(z <= (125 - 100)/15)

= P(z >= 1.67)

= 1 - 0.9525

= 0.0475

Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .

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A) The decimal 2.256 in expanded form and word form are respectively;  2 + 0.2 + 0.05 + 0.006;  Two and three hundred fifty six one - thousandths

B) The decimal 24.09 in expanded form  and word form are respectively; 20 + 4 + 0 + 0.09; Twenty four and 9 one - hundredths.

The expanded form used when writing decimals is the mathematical expression that shows the sum of the values of each digit in the given number.

A) We are given the decimal 2.256

Thus, in expanded form, the given decimal can be expressed as;

2 + (2/10) + (5/100) + (6/1000)

= 2 + 0.2 + 0.05 + 0.006

In word form, we can write the decimal as;

Two and three hundred fifty six one - thousandths

B) We are given the decimal 24.09

Thus, in expanded form, the given decimal can be expressed as;

20 + 4 + (0/10) + (9/100)

= 20 + 4 + 0 + 0.09

In word form, we can write the decimal as;

Twenty four and 9 one - hundredths.

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The width of the photograph is 10 inches if the length of the photograph is 3 inches.

Any arbitrary reference standard for measuring length that has gained acceptance is referred to as a unit of length. The metric system, which is adopted by every nation on earth, is the most prevalent system in use today. The US customary units are also used in the US. The United Kingdom and a few other nations continue to utilize British Imperial units for specific purposes. SI units and non-SI units are subsets of the metric system.

Given,

The expression is:

x(x + 3) = 70

x² + 3x = 70

Now, we have to subtract 70 on both the sides, we get:

x² + 3x - 70 = 0

(x-7)(x + 10) = 0

x-7=0

x=7

x+10=0

x= -10

Since distance cannot be negative, the correct answer is x = 7. We are now plugging in the length (x + 3).

=x + 3

=7 + 3

=10

Therefore, the width of the photograph is 10 inches.

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MCN= ACN-ACN-1 is the basis of diminishing marginal utility.

What is marginal utility?

The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility. Economists utilize the idea of marginal utility to estimate the quantity of a good that consumers will buy.

When the overall utility is increased by the consumption of an additional item, positive marginal utility occurs. On the other side, negative marginal utility arises when the overall utility is reduced by the consumption of one extra unit.

According to the law of diminishing marginal utility, as consumption rises, the marginal utility gained from each additional unit decreases, all other things being equal. The incremental improvement in utility brought on by consuming one more unit is known as marginal utility. An economic term for happiness or contentment is "utility."

So

MCN= ACN-ACN-1

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Answer:

Yes

Step-by-step explanation:

The pair of congruent angles needs to be included between the congruent sides. Since this is not the case, more information is needed.

The correct response is yes, the additional information is needed to show that ΔDEF is congruent to ΔGHJ by SAS congruency rule is whether the sides DE and GH, are congruent

The SAS (Side-Angle-Side) congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

The specified information for each triangle, starting from the indicated angle, and calling the sides in a clockwise direction, we get;

∠E, side EF and side DF in triangle ΔDEF are congruent to angle ∠H, side HJ, and side GJ

Therefore, the information from the diagram in the question are a nonincluded angle and two sides, SSA, which is not a condition for congruency.

The additional information needed to prove ΔDEF is congruent to ΔGHJ, by SAS are the sides DE and GH, which makes the angle ∠E and ∠H included angles.

Therefore, additional information is required;

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