adam is racing around a circular running track. the time he takes to run each lap is 5 seconds less than he took for the previous one. he completes the first lap in 1 minute and 58 seconds. how long (in seconds) does he take to run his seventh lap?

28sinθ is the maximum area of the triangle

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The two sides of triangle are of length 7 and 8.

Triangle has an included angle has a measure of θ degrees.

We need to find the maximum area

A=1/2×7×8×sinθ

A equal to one by two time of seven times of eight times sin theta.

A=7×4×sinθ

A=28sinθ

Hence, 28sinθ is the maximum area of the triangle

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A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years.

a) The hypotheses that can be used to challenge the validity of the claim made by the shareholders' group.

H₀ : u ≤ 9

Hₐ : u > 9

So, the correct option is option (A).

b) T- statistic value is -2.571 for a sample of 90 companies.

c) The critical value for t i.e P-value is 0.0059

d) P-value < α = 0.01, implies reject the null hypothesis. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid. So, the correct option is option(D).

We have given that,

x-bar= 7.27 , σ = 6.38, n = 90

a) Test that the mean tenure for a chief executive officer (CEO) was atleast nine years .

Null and alternative hypothesis is

H₀ : u <= 9

Hₐ : u > 9

b) test statistic:

t =( x-bar - μ ) /σ/√n

=> t = (7.27 - 9 )/6.38/90

=> t = - 1.73/0.67251

=> t = -2.571

c) P-value :

P-value = P( tₙ₋₁ < t) = P(t₉₀₋₁ < t )

=> P-value = P( t₈₉< - 2.571)

=>P-value = P( t₈₉ >2.571)

=> P-value = 1 - P( t₈₉< 2.571)

P-value = 1 - 0.9941 = 0.0059

d) Significance level, = 0.01

we see that p-value= 0.0059 < 0.01

Decision : Reject the null hypothesis H₀

We have no evidence to support the claim.

Hence, we calculate all the required result.

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Complete Question :

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.27 yearsfor CEOs with a standard deviation of

s = 6.38 years.

(a)Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. multiple choice:

i)H0: μ ≤ 9

Ha: μ > 9

ii)H0: μ ≥ 9

Ha: μ < 9

iii) H0: μ > 9

Ha: μ ≤ 9

iv)H0: μ < 9

Ha: μ ≥ 9

v) H0: μ = 9

Ha: μ ≠ 9

(b)Assume 90 companies were included in the sample. What is the test statistic? (Round your answer to three decimal places.)

c)What is the p-value for your hypothesis test? (Round your answer to four decimal places.)

p-value =

(d) At = 0.01,what is your conclusion? MULTIPLE CHOICE:

Answer:

y < -1x + 2

y [tex]\geq \\[/tex] 2x + 4

Step-by-step explanation:

The steps taken to find the two inequalities are on the GraphInequalities worksheet.  The derived equations are graphed on DESMOS and attached, for comparison.

The basic steps are to find the slopes of the two lines and to identify the y-intercepts from the graph.  The inequalities can be assigned based on the darkened areas and presence of either a solid or dashed line.  All are outlined in the worksheet.

Answer: x < 5/3

Step-by-step explanation:

-(4x + 20) < −7(x + 15/7) ............................ Question

-4x - 20 < -7(x + 15/7) ................................ Distribute

-4x - 20 < -7x - 15 ...................................... Distribute

-4x - 20 + 20 < -7x - 15 + 20 ................... Add 20 to both sides

-4x < -7x + 5 ............................................... Simplify

-4x + 7x < -7x + 5 + 7x ............................. Add 7x to both sides

3x < 5 .......................................................... Simplify

3x / 3 < 5 / 3 .............................................. Divide both sides by the same factor

x < 5/3 ......................................................... Simplify

the truth table of expression (A+B).A is T ,T ,F,F . A truth table has one column for each input variable (such as P and Q) and a final column that lists all potential outcomes.

Truth tables are mathematical tables that are used in logic, specifically in relation to Boolean algebra, Boolean functions, and propositional calculus. They contain the functional values of logical expressions on each of their functional arguments, or more specifically, for each combination of values that their logical variables can take.

given

( A+B) . A

A          B      (A + B)      (A+B).A

T           T         T                  T

T           F         T                 T

F           T         T                 F

F           F         F                 F

So , the truth table of expression (A+B).A is T ,T ,F,F .

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Answer:

Step-by-step explanation:

Answer:

the answer is number three

Step-by-step explanation:

820×10 = 8200

The value after double integration is 45.73

We can evaluate rectangle integrals in any order we like in Cartesian coordinates. We treat the other integral as a constant regardless of which integral we assess first; this is something to keep in mind while choosing the order of integration.

We want that x to be constant; we can easily integrate with respect to y. So we will evaluate y first. We get:

[tex]\int\limits^ \int\limits^ \frac{6x}{1+xy} dA=6\int\limits^6_0 \int\limits^1_0 {\frac{x}{1+xy} } \, dydx[/tex]

[tex]or, 6\int\limits^6_0 {[In(1+xy)}_{0} ^{1} ]} \, dx[/tex]

[tex]or, 6\int\limits^6_0 {In(1+x)} } \, -In 1dx[/tex]

[tex]or, 6\int\limits^6_0 {In(1+x)} } \, dx[/tex]

[tex]or,[(1+x)In(1+x)-(1-x)]^{6} _{0}[/tex]

[tex]or,[7In7-In1-7+1]\\or,6(7In7-6)\\or,45.73[/tex]

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The graph that shows the function with the determined behavior is the last graph, circled on the image given at the end of the answer.

The graph of a function is classified as either increasing, decreasing or constant, as follows:

Hence the fourth graph on the image given at the end of the answer is the one with the desired behavior on each interval.

The graphs are given by the image shown at the end of the answer.

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The system of equations is:

2b + 4.25s = 53.75

b - s = 5  

The number of bagels bought is 12 and the number of sandwiches bought is 7.

2b + 4.25s = 53.75 equation 1

b - s = 5  equation 2

Where:

The elimination method would be used to determine the required values.

Multiply equation 2 by 2

2b - 2s = 10 equation 3

Subtract equation 3 from equation 1 :

6.25s = 43.75

Divide both sides of the equation by 2.25

s = 43.75 / 6.25

s = 7

Substitute for s in equation 1:

2b + 4.25(7) = 53.75

2b + 29.75 = 53.75

2b = 53.75 - 29.75

2b = 24

b = 24 / 2

b = 12

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Using law of cosines, the group that is farther from the locker room is; Group B

The law of cosines gives that;

c² = a² + b² - 2ab cos C

Now, for group A, we can use law of cosine to find their current distance from the locker room as;

a² = 4.6² + 2.1² - 2(4.6*2.1)*cos 40°

a² = 21.16 + 4.41 - 14.8

a = √10.77

a = 3.28 miles

Similarly, for Group B, we have;

b² = 4.6² + 2.1² - 2(4.6*2.1)*cos 50°

b² = 21.16 + 4.41 - 12.42

b = √13.15

b = 3.63 miles

This means that group B is farther from the locker room

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Answer:

[tex]y > 3+\frac{x}{2}[/tex]

Hope this helps!

Answer: x<2y-6

Step-by-step explanation:

x-2y<-6

=(x-2y)+6<-6+6

=x-2y+6<0

=(x-2y+6)+(2y-6)<2y-6

=x-2y+6+2y-6<2y-6

=x-2y+2y+6-6<2y-6

=x<2y-6

We are 67% confident that the proportion of students who are tell me that they did their homework over the weekend.0.087 with a margin of error of 0.0175

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

87/1000 = 0.087

We have a 67% confidence level that the percentage of left-handed students is 0.087, with a 0.0175 margin of error.

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The fence Ben paints is 150 square feet.

Given:

ratio of the amount of work allen does to the amount of work ben does is 3:5

allen : ben = 3:5

total work done in ratio = 3 + 5 = 8

Count the fence Ben paints

Since , fence requires a total of 240 square feet to be painted

Thus, ben = ratio of ben/ total ratio × total of works

ben = 5/8 × 240

ben = 1,200/8

ben = 150

Hence , The fence Ben paints is 150 square feet .

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The inverse matrix R⁻¹ does not exist

The inverse of a matrix written as A⁻¹ is such that when the inverse matrix multiplies A, the result is the identity matrix.

Given the matrix [tex]R = \left[\begin{array}{ccc}0&0\\1&3\end{array}\right][/tex], to determine if this matrix has an inverse it must satisfy the following condition.

For a matrix A to have an inverse, its determinant must not be equal to zero. That is det(A) ≠ 0

So, to determine if the above matrix has an inverse, its determinant must not equal zero.

So, the determinant of the matrix det(R) = 0 × 3 - 0 × 1

= 0 - 0

= 0

Since the determinant equals zero, thus we see that its inverse R⁻¹ does not exist

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The percent decrease in the number of people who went to the pool over these four weeks is 30%.

From the information given, in the the first week of July, a record 1060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 348 fewer people went to the pool than in the third week

The total number of people at the end of the week will be:

= 1060 - 100 + 130 - 348

= 742

The percentage decrease will be:

Decrease / Original value × 100

= (1060 - 742) / 1060 × 100

= 30%

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The system of equations which is used to find out the cost of each item (i.e cotton candy and funnel cake) bought by two families McCartney and Lennon Family is

3c + 2f = $24

2c + 4f = $32

We have given that

McCartney family bought

total number of bags of cotton = 3

total number of funnel cakes = 2

total cost of 3 bags and 2 funnel cakes is $24.

Lennon Family bought

total number of bags = 2

total number of funnel cake = 4

total cost of 2 bags and 4 funnel= $32

we have to find out the system of equations which used to find the cost of each item.

let the cost of each funnel cake be f and cotten candy be c .

then, using the above data we get

3c + 2f = $24 ---(1)

2c + 4f = $32 --(2)

Hence, equation (1) and (2) make a system of linear equations which is used to determine the cost of each item.

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Complete question:

HEME At the circus, the McCartney family bought 3 bags of cotton candy and 2 funnel cakes for $24. The Lennon Family bought 2 bags of cotton candy and 4 funnel cakes for $32. Which system of equations could be used to find the cost of each item? Let f represent funnel cake and c represent cotton candy

The length of the side AB represented by x in the triangle ABC is equal to 16 using the trigonometric ratio of sine.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

The triangles ABC and ADB are right-angled triangles, we shall be considering the trigonometric ratio of the sine of angle A which is common to both triangles.

For triangle ABC;

sinA = adjacent/hypotenuse

sinA = x/32

for triangle ADB;

sinA = 8/x

thus we can say that;

x/32 = 8/x {cross multiplication}

x² = 3 × 32

x² = 256

x =√256 {take square root for both sides}

x = 16.

Therefore, 16 is the length of the side AB labelled x, using the trigonometric ratio of sine of the common angle A to the triangles ABC and ADB.

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Answer:

are you stupif? no dumas

Step-by-step explanation:

The value of the function h(x) = -3(x - 1) + 4 when x is -5 is 19.

It is important to note that a function is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, the function is given a :

h(x) = -3(x - 1) + 4

When x = -5. This will be:

h(-5) = -3(-5 - 1) + 4

= -3(-6) + 1

= 18 + 1

= 19

The value is 19.

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The linear equation that represents the total cost of the gas will be y = 15.7x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The cost of two gallons of gas is $31.40. Then the rate (slope) is given as,

m = $31.40 / 2

m = $15.7 for each gallon

Let 'x' be the number of gallons of gas and 'y' be the total cost. Then the equation is given as,

y = 15.7x

The linear equation that represents the total cost of the gas will be y = 15.7x.

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If the 34% of the college students major in STEM than the probability that exactly 15 of them major in STEM is 0.1162   .

In the question ,

it is given that ,

percent of students that major in STEM is = 34% ;

that means , p = 0.34 ; so , q = 0.6

number of students randomly selected (n) = 40 ,

By the Binomial Probability Distribution ,

we get ;

p(x = 15) = ⁴⁰C₅*(0.34)¹⁵*(0.66)²⁵

Simplifying the above value further ,

we get ;

p(x = 15) = 0.1162 .

Therefore , the required probability is 0.1162 .

The given question is incomplete , the complete question is

The 34% of all college students major in stem (science, technology, engineering, and math). if 40 college students are randomly selected, find the probability that exactly 15 of them major in stem  .

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The conclusion that can be made from the given observations is that the dew factor temperature is 90% of the air temperature.

Humidity is the quantity of water vapor withinside the air. If there is lots of water vapor withinside the air, the humidity might be high.

The temperature have to upward push so as for air to come to be saturated with water vapor.

The air holds little water vapor and is rather dry.

The quantity of water vapor withinside the air is 90% of what the air can hold.

The dew factor temperature is 90% of the air temperature.

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False, the zip codes of a sample of 345 customers at pet shop are not an example of qualitative variables

The zip codes of a sample of 345 customers at a pet shop are an example of quantitative variables because they are numerical values that can be measured and compared. Qualitative variables, on the other hand, are categorical variables that describe a characteristic or attribute of a person, place, or thing, such as gender, color, or nationality. They cannot be measured numerically and are often described using words or labels.

Qualitative Variables: Qualitative variables are variables that are not numerical or quantifiable. Examples of qualitative variables include gender, race, eye color, ethnicity, nationality, marital status, and religious preference.

Quantitative Variables: Quantitative variables are variables that are numerical or quantifiable. Examples of quantitative variables include height, weight, age, income, income level, GPA, number of children, and number of hours worked.

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Answer:

252 in.²

Step-by-step explanation:

12 in. by 21 in. rectangle

The 6 in. by 3 in. rectangle missing on the left bottom corner is made up by the same-sized rectangle on the right side.

A = LW

A = 21 in. × 12 in.

A = 252 in.²

Answer: lines j and k are perpendicular

Step-by-step explanation:

Let's find the equations of lines j and k

                       [tex]\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

Line j: (8,2)  (-2,-2)

x₁= 8     x₂=-2    y₁=2     y₂=-2

[tex]\displaystyle\\\frac{x-8}{-2-8}=\frac{y-2}{-2-2} \\\\\frac{x-8}{-10}=\frac{y-2}{-4} \\\\[/tex]

 Multiply both parts of the equation by -4:

[tex]\displaystyle\\\frac{2}{5} (x-8)=y-2\\\\\frac{2}{5} x-\frac{16}{5} =y-2\\\\\frac{2}{5} x-3.2+2=y-2+2\\\\\frac{2}{5}x-1.2=y\\\\ Thus,\ y=\frac{2}{5}x-1.2[/tex]

Line k: (-4,3)   (-6,8)

x₁=-4    x₂=-6    y₁=3    y₂=8

[tex]\displaystyle\\\frac{x-(-4)}{-6-(-4)} =\frac{y-3}{8-3} \\\\\frac{x+4}{-6+4}=\frac{y-3}{5} \\\\\frac{x+4}{-2} =\frac{y-3}{5}[/tex]

Multiply both parts of the equation by 5:

[tex]\displaystyle\\-\frac{5}{2}(x+4)=y-3\\\\ -\frac{5}{2}x-10=y-3\\\\ -\frac{5}{2}x-10+3=y-3+3\\ -\frac{5}{2}x-7=y\\Thus,\ y=-\frac{5}{2} x-7[/tex]

Hence, lines j and k are perpendicular

Answer:

1.   d = 40; 2 irrational

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions.\\\end{minipage}}[/tex]

Given quadratic equation:

[tex]3x^2+4x-2=0[/tex]

Therefore:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned}\implies b^2-4ac&=(4)^2-4(3)(-2)\\&=16-12(-2)\\&=16+24\\&=40\end{aligned}[/tex]

Therefore, as d = 40 and 40 > 0:

[tex]\implies b^2 - 4ac > 0 \implies \text{two real solutions}.[/tex]

To determine if the solutions are irrational or rational, simply square root the discriminant.

[tex]\implies \sqrt{d}=\sqrt{40}=2 \sqrt{10}[/tex]

As the discriminant is not a perfect square, then its square root is irrational and so the solutions of the quadratic equation are irrational.

After subtracting the fractions, we know that Jordan runs 1/24 miles more on Monday than Tuesday.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction.

The numerator of a proper fraction is less than the denominator.

So, we know that:

Jordan runs on Monday: 7/8 miles

Jordan runs on Tuesday: 5/6 miles

Jordan runs more on Monday:

7/8 - 5/6

3*7 - 4*5/24

21 - 20/24

1/21 miles

Therefore, after subtracting the fractions, we know that Jordan runs 1/24 miles more on Monday than Tuesday.

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Correct question:
Jordan ran 7/8 miles on Monday and 5/6 miles on Tuesday.

How much farther did Jordan run on Monday than on Tuesday?

Enter your answer as a fraction in simplest form.