estimate the area under the curve given the following fuction, interval, and number of subintervals using the right endpoint method.

1) The probabilities are given as follows:

a) More than 75: 0.0301 = 3.01%.

b) Between 60 and 73: 0.4484 = 44.84%.

c) Less than 50: 0.1057 = 10.57%.

2) The proportion of students who fail the module is of: 0.0062 = 0.62%.

3) The measures are given as follows:

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

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

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

[tex]\mu = 60, \sigma = 8[/tex]

The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:

Z = (75 - 60)/8

Z = 1.88

Z = 1.88 has a p-value of 0.9699.

1 - 0.9699 = 0.0301 = 3.01%.

The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:

Z = (73 - 60)/8

Z = 1.63

Z = 1.63 has a p-value of 0.9484.

Z = (60 - 60)/8

Z = 0

Z = 0 has a p-value of 0.5.

Then:

0.9484 - 0.5 = 0.4484 = 44.84%.

The probability of an score less than 50 is the p-value of Z when X = 50, hence:

Z = (50 - 60)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1057.

The proportion who might fail the test is the p-value of Z when X = 40, hence:

Z = (40 - 60)/8

Z = -2.5

Z = -2.5 has a p-value of 0.0062.

Then the statistical measures are obtained as follows:

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The measure of the angle ∠BDC is 68°.

What is the straight line angle?

A straight angle in geometry is one that is 180 degrees in length. It looks like a straight line, which is why it is known as a straight angle. In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.

We have,

∠BDA is a straight angle

so ∠BDA = 180°

We need to find the ∠BDC

∠CDA = -8x + 48°

∠BDC = -7x + 12°

∠BDA = ∠BDC + ∠CDA = 180°

(-8x + 48°) + (-7x + 12°) = 180°

-15x + 60° = 180°

-15x = 120°

x = -8°

∠BDC = -7x + 12°

= -7(-8°) + 12°

= 56° + 12°

= 68°

Hence, the measure of the angle ∠BDC is 68°.

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The given statement is true.

How it is true ?

Because if the matrix of coefficients of a homogenous system of n linear equations is non-singular then there will be the inverse for that matrix.

We know ,

If matrix is non-singular then it has unique solution

and if it singular then it has either no-solution or infinite solution.

So, the above statement is always true.

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Using the conversion factor we know that the penguin gained 5,350 grams of weight from a chick to an adult.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

So, we know that:

1 kg = 100 g

Weight of the adult penguin: 5 1/2 kg that is,

5 1/2 = 10+1/2 = 11/2 = 5.5

5.5kg = 5500 g

Weight of the newborn penguin: 150 g

Weight gain from chick to adult:

5500 - 150

5,350 g

Therefore, using the conversion factor we know that the penguin gained 5,350 grams of weight from a chick to an adult.

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The flagpoles are 40 feet, and the wires cross at E, which is directly above point F on the ground. Then EF is 5.142 feet.

The maximum height for flagpoles is twenty (20) feet. (3) When next to or encircled by residential lots, the flagpole may not be erected in any side or rear yard setback.

It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

by applying similar triangles on triangles we get the equation on ABC and EFC

40y+9x=360

by applying similar triangles on triangles, we get the equation on DBC and EBF

y=3/10x

x=120/7

putting values in the very first equation we get

y=3/10x(120/7)

y=5.142

EF=5.142 feet.

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Answer:

18

Step-by-step explanation:

72/12=6

6×3=18

.....

Valeria rode for 15 miles in the evening each day.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Valeria has been training for the Charlestown Cruisers bike race. The first week she trained, she rode 5 days and took the same two routes each day. She rode an 8-mile route each morning and a longer route each evening. By the end of the week, she had ridden a total of 115 miles.

Let the distance she covered in evening be x,

Establishing the equation,

(8+x)5 = 115

8+x = 23

x = 15

Hence, Valeria rode for 15 miles in the evening each day.

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Answer: 227

Step-by-step explanation: (5 + 4 ) = 9                                                      

= 3 x 9^2 - 4^2

9^2 = 81

= 3 x 81 - 4^2

4^2 = 16

= 3 x 81 - 16

3 x 81 = 243

= 243 - 16

243 - 16 = 227

= 227.

The value of x satisfying the equation 1.5(x + 4) - 3 = 4.5(x - 2) is : -

1.5(x + 4) - 3 = 4.5(x - 2)

Using the distributive property, multiply the terms in the equation.

1.5x + 1.5 × 4 - 3 = 4.5x - 4.5 × 2

1.5x + 6 - 3= 4.5x - 9

Isolate the variable x using transposing method

4.5x - 1.5x = 6 - 3 + 9

3x=15-3

3x = 12

Therefore,  x = 12/3 = 4

The value of x satisfying the equation 1.5(x + 4) - 3 = 4.5(x - 2) is 4.

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The congruence statement for the triangle is that they gave same sides and angles.

When the three sides and three angles of two triangles are equal in any orientation, they are said to be congruent.

According to the Side Side Side (SSS) Theorem, if all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are congruent.

It should be noted that from the triangle given, the sides and angles are the same. This was illustrated. This illustrates the congruence and the triangle was reflected.

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The side lengths of the new phone are proportional to the old phone, then the width of the new phone is 5.125 inches.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The dimensions of the older phones are,

Length, L(1) = 1.4 inches

Width, W(1) = 4.1 inches

The dimensions of the new phone are,

Length, L(2) = 1.75 inches

Width, W(2) = ?

Then the width of the new phone is,

1.4 × W(2) = 4.1 × 1.75

W(2) = (4.1 × 1.75)/1.4

W(2) = 5.125 inches.

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Answer:

I am not exactly sure what they want you to put in the boxes, but hopefully the explanation below will shed some light on what is going on with this problem.

Step-by-step explanation:

The equation would be

y = 3x  

It looks like your question wants you to write the equation in the form

r(x) = 3x

y would be the student's score on the test.

x would be the number of questions that the student got right.

The x is the independent variable.  It tells us how many questions the student got right.

The y is the dependent variable.  It is the student's score.  The student's score depends on how many questions the student got right.

R(25) is saying what would be the score if the student got 25 answer correct?

3(25) = 75.  The student would get a score of 75

[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}[/tex]

Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.  A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French. 

There are 3 solutions  to the system of equations

1)single solution

2)infinite solutions

3)no solutions

Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

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The degree of freedom value for the A× B intersection is  = 6.72

The F value is the value of the F distribution. Various statistical tests generate F values. You can orrect answer is use this value to determine whether your test is statistically significant.

The F value is used in the analysis of variance (ANOVA). It is calculated by dividing the two mean squares. This calculation determines the ratio of explained to unexplained variance.

The F distribution is a theoretical distribution. There are many types of these distributions, each with different degrees of freedom.

Determines the probability of the F value using the degrees of freedom of the F value and the variance source. The probability is the significance value of the test.

AxB intersection:

Interpreting the output of the general linear model command focuses on two parts: the means table and the ANOVA summary table. The average table is the focus of the analysis, while the summary table draws attention to the interesting or statistically significant parts of the average table.

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The number with the given features in this problem is given as follows:

36.

First we consider that the number is a square number, meaning that it has a perfect square root.

The number is between 10 and 99, hence the possible square numbers between 10 and 99 are given as follows:

The numbers with a sum of the digits of 9 are given as follows:

The factors of each number are given as follows:

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From the compound inequality explained below in concept, it has been proven that compound inequality has a solution of all real numbers except 3.5.

We are given the inequalities as;

5x – 3 > 14.5 or (2x + 5)/3 < 4

For the first inequality;

Add 3 to both sides to get;

5x > 17.5

Divide both sides by 5 to get;

x > 3.5

For the second inequality, we have;

(2x + 5)/3 < 4

Multiply both sides by 3 to get;

2x + 5 < 12

Subtract 5 from both sides to get;

2x < 7

Divide both sides by 2 to get;

x < 3.5

The first inequality gives the solution as x > 3.5.

The second inequality gives the solution as x < 3.5.

The solution of an “or” compound in equality is everything in both solution sets, so the solution set is all of the numbers less than 3.5 and greater than 3.5. Since neither of the inequalities includes 3.5, the compound inequality has a solution of all real numbers except 3.5.

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The number of infected students after 5 days = 694

The number of infected students  with respiratory virus is modeled by an exponential function f(t) = 25000 /1+332e^(-0.45t) where time t, is measured in days.

We need to find the number of students infected with the virus after 5 days.

For t = 5,

f(5) = 25000 /1+332e^(-0.45 * 5)

f(5) = 25000 /(1+332*0.1054)

f(5) =  25000 /35.9928

f(5) = 694.58

f(5) ≈  694

Therefore, the number of students infected with the virus after 5 days = 694

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The complete question is:

75 students are currently infected with respiratory virus- that is spreading through a population of college students_ The number of infected students is modeled by f(t) = 25000 /1+332e^(-0.45t) where time; t, is measured in days. How many students are predicted to be infected with the virus after 5 days? Round your answer to the nearest whole number.

Answer:

4 is the smallest number

Step-by-step explanation:

4 times 8 is 32. 4 + 8 is 12. 4 is smaller than 8 so it would be the smaller number

Although part of your question is missing, you might be referring to this full question: If P is the incenter of ΔJKL, find each measure (triangle as attached).

Based on the property of incenter, the measurements of the sides and the angles will be:

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m∠K = 36°

By using the property of incenter:

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

By using the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

Then, from ΔJMP,

tan(32°) = MP/MJ

tan(32°) =  7/MJ

MJ =  7/tan(32)°

MJ = 11.20

And from ΔPOL,

tan(22°) = OP/OL

tan(22°) = 7/OL

OL = 17.33

And from ΔKNP,

tan(36°) = NP/KN

tan(36°) = 7/KN

KN = 9.63

Hence, JK = MJ + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

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It is false that if the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular

The augmented matrix is an extension of a matrix in which we add a column ( non homogeneous part of the system)

Say , Ax = b

Here , b is column part

So , Augmented matrix will be [ A : b ]

The Rank of augmented matrix can be found by performing elementary row operations on a augmented matrix and counting the number of the rows without zero comparing the rank of an augmented matrix

The rank of coefficient matrix can determined if there is a  solution to the system of solution

In the question this statement,

If the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular is false

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There are No Real Roots possible for the Quadratic Equation

What is Quadratic Equation?

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. where x is an unknown variable and the numerical coefficients a, b, and c.

Solution:

x² - 12x + 52 = 0

Formula to Solve the equation is -b +- (D) / 2a

D is the discriminant

D = √b² - 4ac

D = √12*12 - 4*52

D = √144 - 208

D = √-64

Since the value of Discriminant is negative

Therefore there are no real roots possible for the equation

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Answer:

Step-by-step explanation:

Answer:

f(6) = 21

Step-by-step explanation:

f(6) = 3x + 3

f6) = 3(6) + 3

f(6) = 18 + 3

f(6) = 21

Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.

To find an unknown quantity in a problem we use the algebraic expression. These are combinations of variables and constant terms. Here variables are used to represent the Unknown Numbers.

Here we have

Martina, Ahmad, and Ryan served a total of 87 orders

Since we don't how many orders served each one

Let's assume that each of them with different variables

Martina served 'm' orders

Ahmad served 'a' orders

Ryan served 'r'

Given that

Ahmad served 9 fewer orders than Martina  

=> a = m - 9 ---- (1)

Ryan served 2 times as many orders as Martina.

=> r = 2m --- (1)    

Given that total served orders = 87

=> m + a + r = 87

=> m + m - 9  + 2m = 87        [ from (1) and (2) ]

=> 4m = 87 + 9

=> 4m = 96

=> m = 24

Number of orders served by Ahmad, a = 24 - 9 = 15  

Number of orders served by Ryan, r = 2(24) = 48

Therefore,

Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.

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The answer is A & C

To determine if a set of ordered pairs represents a function, you can check if each input (x value) is associated with only one output (y value).

In set A, input 4 is paired with output 1 and input 8 is paired with output 2. These two inputs are paired with only one output, so the set A can represent a function.

In set B, input -2 is paired with two different outputs.

-1 and 5. This means that -2 has multiple exits, so set B does not represent a function. In set C, input 7 is paired with output 4 and input 8 is paired with output 3. The set C can represent a function because these two inputs are paired with only one output.

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a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).

(b)The P-value is 0.0068.

To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.

A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.

C.I=x-t(alpha/2)xs/sqrt{n}

=3150+_2.01*250/sqrt{50}

=(3078.9358,3221.0642)

b) P value =P(t<-2.83)+P(t>2.83)

use calculator

                 =0.0034+0.0034

                  =0.0068

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Answer:

A) 40

B) 5

C) 55

D) 35

Step-by-step explanation:

The formula is:

[tex]\frac{(F - 32)5}{9}[/tex]

F is the temperature in Fahrenheit.

A)

[tex]\frac{(104-32)5}{9}[/tex]

40

B)

[tex]\frac{(41-32)5}{9}[/tex]

5

C)

[tex]\frac{(131-32)5}{9}[/tex]

55

D)

[tex]\frac{(95-32)5}{9}[/tex]

35

If you made a pie and then ate two slices of it, the first pie would be missing two slices of pie. If you then made two more slices of pie for another pie, the first pie would be missing a total of four slices of pie. This is because you took two slices of pie from the first pie and added them to the second pie, leaving the first pie with two fewer slices than it originally had.

Answer:

The first pie would be missing four slices in total

Step-by-step explanation:

If you make a pie and then eat two slices of it, there would be two missing slices from the first pie. If you then make two more slices of pie for another pie, the first pie would be missing a total of four slices. The first pie would be missing four slices in total.

Therefore , Scatter plot1 0.342 ,Scatter plot2 -0.994, Scatter plot 3 0.743 ,Scatter plot4 -0.743 and  Scatter plot5 0.994.

An example of a plot or mathematical diagram is a scatter plot, which uses Cartesian coordinates to show the values of typically two variables given a collection of data. One more variable can be presented if the points are programmed.

Here,

The observed data are highly erratic, according to scatter plot 1. The relationship between the two variables is thus weak. There is a 0.342 correlation coefficient.

Observations in the scatter plot 2 are aligned with the straight line. A reduction in y values follows a rise in x values. Therefore, there is a significant negative connection between the two variables. This means that the correlation coefficient is -0.994.

The scatter plot's third scatter plot shows that the observations are slightly yet positively divergent. Consequently, there is a weakly positive connection between the two variables. The correlation coefficient is therefore 0.743.

Scatter plot 4: The observations show a considerably negative deviation from the mean. Consequently, there is a light negative correlation between the two variables. Consequently, the correlational coefficient is -0.743.

Scatter plot 5: The observations are aligned with the straight line in the scatter plot. The matching y values rise as the corresponding x values do. Therefore, there is a significant positive connection between the two variables. So, 0.994 is the correlation coefficient. As follows is the matching table:

Spread layout 1 0.342 Spread plot 2 -0.994 3.743% Scatter plot Dispersion plot4 -0.743 Spread plot5 0.994

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