Aaron sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 96% confidence level, he also found that t* = 2.081.confidence intervat = x±s/√n A 96% confidence interval calculates that the average number of hours of sleep for working college students is between __________.

Answer:

40

Step-by-step explanation:

140 + x  = 3*(100-x)

140 + x = 300 - 3x

x + 3x = 300 - 140

4x = 160.

x = 40.

Answer:

7.2x-5

Step-by-step explanation:

2(3.6x-2.5)

=7.2x-5

PLS GIVE BRAINLIEST

1. 1/6 is the probability of rolling a five on the next roll.

2. The probability of getting 5 fives in a row when rolling a single die is  1/7776 .

3.  1/38 is he probability of 7 coming up on the very next spin is

4. 1/54782 is the probability of getting three 7's in a row on a roulette wheel.

5.  (1/10)⁶ is the probability of getting a 1 on all six trials.

6. 1/36 is the probability of getting a pair of sixes when rolling a pair of dice is

7.  The probability of getting any pair is 1/6

It is a branch of mathematics that deals with the occurrence of a random event.

1. The probability of rolling a five on a single roll of a fair die is 1/6, since there are six equally likely outcomes: rolling a 1, 2, 3, 4, 5, or 6.

the probability of rolling a five on the next roll is still 1/6, regardless of whether the previous rolls resulted in four fives in a row or not.

2. The probability of getting a five on a single roll of a fair die is 1/6, as there are six equally likely outcomes.

the probability of getting 5 fives in a row when rolling a single die is:

(1/6) × (1/6) × (1/6) × (1/6) × (1/6) = 1/7776

3. The probability of any particular number coming up on a single spin of an American roulette wheel with 38 numbers is 1/38, since there are 38 equally likely outcomes.

As these are independent , the probability of 7 coming up on the very next spin is still 1/38.

4. The probability of getting three 7's in a row on a roulette wheel is:

(1/38) × (1/38) × (1/38) = 1/54,872

5. The probability of generating a 1 on a single trial is 1/10.

The probability of getting a 1 on a single trial by itself six times

(1/10)  × (1/10)  × (1/10)  × (1/10) × (1/10)  × (1/10) = (1/10)⁶

The probability of getting a 1 on all six trials is (1/10)⁶

6.

The probability of getting a pair of sixes when rolling a pair of dice is:

1/36

7.

The probability of getting any pair when rolling a pair of dice is:

Number of ways to get a pair / Total number of possible outcomes

= 6 / 36

= 1 / 6

So the probability of getting any pair is 1/6

Hence,

1. The probability of rolling a five on the next roll is 1/6.

2. 1/7776 is the probability of getting 5 fives in a row when rolling a single die.

3. The probability of 7 coming up on the very next spin is  1/38.

4. The probability of getting three 7's in a row on a roulette wheel is 1/54782

5. The probability of getting a 1 on all six trials is (1/10)⁶

6. The probability of getting a pair of sixes when rolling a pair of dice is:

1/36

7.  the probability of getting any pair is 1/6

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Answer:

a) \(a = 2\) and \(b = -4\), b) \(c = -10\), c) \(f(-2) = -\frac{5}{3}\), d) \(y = -\frac{5}{2}\).

Step-by-step explanation:

a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:

1) A root of the polynomial at numerator is -2. (Removable discontinuity)

2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.

We analyze each polynomial by factorization and direct comparison to determine the values of \(a\), \(b\) and \(c\).

Denominator

i) \((x+2)\cdot (x-1) = 0\) Given

ii) \(x^{2} + x-2 = 0\) Factorization

iii) \(2\cdot x^{2}+2\cdot x -4 = 0\) Compatibility with multiplication/Cancellative Property/Result

After a quick comparison, we conclude that \(a = 2\) and \(b = -4\)

b) The numerator is analyzed by applying the same approached of the previous item:

Numerator

i) \(c\cdot x - 5\cdot x^{2} = 0\) Given

ii) \(x \cdot (c-5\cdot x) = 0\) Distributive Property

iii) \((-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0\) Distributive and Associative Properties/\((-a)\cdot b = -a\cdot b\)/Result

As we know, this polynomial has \(x = -2\) as one of its roots and therefore, the following identity must be met:

i) \(\left(x -\frac{c}{5}\right) = (x+2)\) Given

ii) \(\frac{c}{5} = -2\) Compatibility with addition/Modulative property/Existence of additive inverse.

iii) \(c = -10\) Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result

The value of \(c\) is -10.

c) We can rewrite the rational function as:

\(f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}\)

After eliminating the removable discontinuity, the function becomes:

\(f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)\)

At \(x = -2\), we find that \(f(-2)\) is:

\(f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right]\)

\(f(-2) = -\frac{5}{3}\)

d) The value of the horizontal asympote is equal to the limit of the rational function tending toward \(\pm \infty\). That is:

\(y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}\) Given

\(y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right]\) Modulative Property

\(y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right]\) Existence of Multiplicative Inverse/Definition of Division

\(y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)\)   \(\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}\)

\(y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)\)   \(\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}\)/\(x^{m}\cdot x^{n} = x^{m+n}\)

\(y = -\frac{5}{2}\) Limit properties/\(\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0\), for \(n \geq 1\)

The horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\).

Using asymptote concepts, it is found that:

a) Building a quadratic equation with leading coefficient 2 and roots 1 and -2, it is found that a = 2, b = -4.

b) c = -10, since the discontinuity at x = -2 is removable, the numerator is 0 when x = -2.

c) Simplifying the function, it is found that at \(x = -2, f(x) = -\frac{5}{3}\).

d) The equation for the horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\)

-------------------------

Item a:

\(2(x - 1)(x - (-2)) = 2(x - 1)(x + 2) = 2(x^2 + x - 2) = 2x^2 + 2x - 4\)

\(2x^2 + ax + b = 2x^2 - 2x - 4\)

Thus a = 2, b = -4.

-------------------------

Item b:

\(-2c - 5(-2)^2 = 0\)

\(-2c - 20 = 0\)

\(2c = -20\)

\(c = -\frac{20}{2}\)

\(c = -10\)

-------------------------

Item c:

With the coefficients, the function is:

\(f(x) = \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \frac{-5x(x + 2)}{2(x - 1)(x + 2)} = -\frac{5x}{2(x - 1)}\)

At x = -2:

\(-\frac{5(-2)}{2(-2 - 1)} = -\frac{-10}{-6} = -(\frac{5}{3}) = -\frac{5}{3}\)

Thus, simplifying the function, it is found that at \(x = -2, f(x) = -\frac{5}{3}\)

-------------------------

Item d:

The horizontal asymptote of a function is:

\(y = \lim_{x \rightarrow \infty} f(x)\)

Thus:

\(y = \lim_{x \rightarrow \infty} \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \lim_{x \rightarrow \infty} \frac{-5x^2}{2x^2} = \lim_{x \rightarrow \infty} -\frac{5}{2} = -\frac{5}{2}\)

The equation for the horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\)

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Quotient rule of differentiation.

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

d/dx(csc x) = -csc x cot x.

To show that d/dx(csc x) = -csc x cot x, we will use the quotient rule of differentiation.

Recall that csc x is defined as 1/sin x.

Therefore, we can rewrite the function as:

csc x = (sin \(x)^{-1}\)

Taking the derivative of csc x with respect to x using the quotient rule, we get:

d/dx(csc x) = (-1)(sin x) (cos x)

Now we need to simplify this expression using trigonometric identities. Recall that

cot x = cos x/sin x.

Therefore, we can rewrite the above expression as:

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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To show that d/dx(csc x) = -csc x cot x, we need to differentiate csc x with respect to x using the chain rule and trigonometric identities.

Recall that csc x is the reciprocal of sin x, so we can write:

csc x = 1/sin x

Then, using the chain rule, we can differentiate csc x as follows:

d/dx(csc x) = d/dx(1/sin x) = -1/sin^2 x * d/dx(sin x)

Now, we can use the derivative of sin x with respect to x, which is cos x:

d/dx(csc x) = -1/sin^2 x * cos x

Next, we can use the identity cot x = cos x/sin x to simplify the expression:

d/dx(csc x) = -cos x/(sin x)^2 = -csc x * cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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When solving this system of equations by elimination, the resulting equation when the variable y has been eliminated is, 3x = -3.

Hence the correct option is (A).

The given system of linear equations is

9x + 3y = 12 ............... (i)

2x + y = 5 ................. (ii)

We have to solve the system using elimination method by eliminating the variable y first.

Coefficients of y in both equations are 3 and 1 respectively.

So, LCM(3, 1) = 3.

Multiplying the equation (ii) by 3 we get,

3(2x + y) = 3*5

6x + 3y = 15 ............. (iii)

Subtracting the equation (i) from the equation (iii) we get,

6x + 3y - 9x - 3y = 15 - 12

-3x = 3

3x = -3

so the resulting equation when the variable y has been eliminated is, 3x = -3.

Hence the correct option is (A).

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Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

For this problem, the roots are given as follows:

Hence the polynomial is given as follows, considering leading coefficient a = 1:

\(f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)\)

His error was at the application of the minus signal to the complex roots.

Then:

f(x) = (x - 3)[(x - 2)² - (2i)²]

f(x) = (x - 3)(x² - 4x + 4 + 4)

f(x) = (x - 3)(x² - 4x + 8)

f(x) = x³ - 7x² + 20x - 24.

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\(\large\underline{\sf{Solution-}}\)

Given Polynomial:

\( \rm \longmapsto f(x) = {x}^{2} + px - q\)

Let α and β be the zeros of f(x)

Then:

\( \rm \longmapsto \alpha + \beta = - p\)

\( \rm \longmapsto \alpha \beta = - q\)

Now, it's given that:

\( \rm \longmapsto k = \dfrac{ \alpha }{ \beta } \)

Consider the expression given:

\( \rm = \dfrac{k}{1 + {k}^{2} } \)

\( \rm = \dfrac{ \dfrac{ \alpha }{ \beta } }{1 + { \dfrac{ \alpha {}^{2} }{ \beta {}^{2} } }} \)

\( \rm = \dfrac{ \dfrac{ \alpha }{ \beta } }{ { \dfrac{ \alpha {}^{2} + { \beta }^{2} }{ \beta {}^{2} } }} \)

\( \rm = \dfrac{ \alpha }{ { \dfrac{ \alpha {}^{2} + { \beta }^{2} }{ \beta } }} \)

\( \rm = \dfrac{ \alpha \beta }{\alpha {}^{2} + { \beta }^{2} } \)

\( \rm = \dfrac{ \alpha \beta }{ {( \alpha + \beta )}^{2} - 2 \alpha \beta } \)

\( \rm = \dfrac{ - q }{ {p}^{2} + 2q} \)

According to the figure, the arc lengths are

The missing sides in the figure are sought knowing that central angles are equal to length of arcs. Hence we have that

arc CE = 180 degrees - arc CA

arc CE = 180 degrees - 50 degrees

arc CE = 130 degrees

arc DE = arc CA (vertical angles)

arc DE = 50 degrees

arc FAE = 360 degrees - 90 degrees

arc FAE = 270 degrees

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The inequality that describes these points is y ≤ -1/2(x) -3. The graph is given the attachment.

To graph a linear inequality in two variables (say, x and y), start with y on one side. Consider the related equation obtained by changing the inequality sign to an equality sign. This equation's graph is a straight line.

If the inequality is strict (< or >), draw a dashed line. If the inequality is not strict (≤ or ≥), draw a solid line.

Finally, choose one point that is not on either line ((0,0) is usually the easiest) and determine whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.

Graph each of the system's inequalities in a similar way.

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The discharge of the river is 150 cubic meters per second, which means 150 cubic meters of water are flowing through this river every second.

When Q, V, and A are substituted for the discharge, stream velocity, and cross-sectional area of the river, respectively, the result is the discharge, which can be computed using the formula Q = V x A.

In this instance, the river has a cross-sectional area that is 75 metres squared and is 15 metres broad by 5 metres deep.

Hence, Q = 2 metres per second x 75 metres squared = 150 cubic metres per second is the river's discharge.

The river's discharge, which in this example is 150 cubic metres per second, is a measurement of how much water flows through the river in a specific amount of time. This indicates that this river receives 150 cubic metres of water each second.

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The exact value of the expression is: sin(182°) ≈ -0.1492 (rounded to four decimal places)

To write this expression as a trigonometric function of a single number:

We can use the addition formula for sine and cosine:

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

Using these expressions, we can rewrite the expression as follows:

sin(11° + 190°) + sin(19°)

Simplifying the first term using the identity sin(a + 180°) = -sin(a),

we get:

sin(201°) - sin(19°)

Now, using the subtraction formula for sine, we can write:

sin(a - b) = sin(a) cos(b) - cos(a) sin(b)

Therefore,

sin(201° - 19°) = sin(182°)

So the exact value of the formula:

sin(182°) ≈ -0.1492 (rounded to four decimal places)

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Answer:

180

Step-by-step explanation:

A 3-digit number cannot start with 0, so the leftmost digit is a choice of 6 digits out of the 7. The middle digit can be chosen from all 7 digits minus the one already used, so there are 6 choices. The right digit can be chosen from 5.

6 × 6 × 5 = .180

The number of three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 is 180.

This can be calculated by finding the number of element availabe at first place which is 6 excluding 0 than for second position 6 as first number is excluded and 0 is added and for the last positon the number of possibe combination is 5 as 2 digits are already used.

The final answer is 6*6*5 = 180

so count of 3 digit numbers that can be formed by the given set of digit without repetetion allowed is  180

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The shortest length of cable needed is approximately 3464 ft.

.To find the shortest length of cable needed for the cable car running to the top of the mountain. We'll use the terms: mountain height (3400 ft), inclined angle (74 degrees), and distance from the base (1000 ft).

Step 1: Draw a right triangle where the hypotenuse represents the cable, the vertical leg represents the mountain's height (3400 ft), and the horizontal leg represents the distance (1000 ft) from the base of the mountain.
Step 2: We are given the inclined angle (74 degrees) between the hypotenuse and the horizontal leg. We can use the sine function to find the ratio between the height (opposite leg) and the length of the cable (hypotenuse).

\(sin(74 degress) = \frac{height}{hypotenuse}\)
Step 3: Plug in the height (3400 ft) and solve for the hypotenuse.

\(sin(74 degress) = \frac{3400}{hypotenuse}\)
\(hypotenuse = \frac{3400}{sin(74 degrees)}\)
Step 4: Calculate the value hypotenuse = 3464.45 ft
Step 5: Round the answer to the nearest foot.

The shortest length of cable needed is approximately 3464 ft.

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According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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1720 gallons of rainwater are needed to fill the container to the top.

What does have capacity mean?

The ability to use and comprehend data to make decisions and convey those decisions is referred to as capacity.

If the container is 30% filled with rainwater, then it is 70% empty. Let's first calculate the capacity of the container when it is 100% full:

Capacity of container = (100 / 30) * 1290 = 4300 gallons

So, the container has a capacity of 4300 gallons when it is 100% full.

Since the container already has 30% of its capacity filled with rainwater, we need to add enough rainwater to fill the remaining 70% of the capacity. The amount of rainwater needed to fill the container to the top is:

Amount of rainwater needed = 70% of 4300 - 30% of 4300

= 0.7 * 4300 - 0.3 * 4300

= 3010 - 1290

= 1720 gallons

Therefore, 1720 gallons of rainwater are needed to fill the container to the top.

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Answer:

Summary:

Step-by-step explanation:

We know that the diagonals of a parallelogram bisect each other.

As

The parallelogram PQRS is given, so

RT = TP

Given

plug in RT = x and TP = 5x-28 in the equation RT = TP

RT = TP

x = 5x-28

switch the sides

5x-28 = x

adding 28 in both sides

5x-28+28 = x+28

simplify

5x = x+28

subtract x from both sides

5x-x = x+28-x

4x = 28

divide boh sides by 4

4x ÷ 4 = 28  ÷ 4

simplify

x = 7

Therefore, we conclude that the value of x is: x = 7

Similarly,  

QT = TS

Given

plug in QT = 5y and TS = 2y+12 in the equation QT = TS

QT = TS  

5y = 2y+12

subtract 2y from both sides

5y - 2y = 2y+12-2y

simplify

3y = 12

divide both sides by 3

3y ÷ 3 = 12 ÷ 3

simplify

y = 4

Therefore, we conclude that the value of y is: y = 7

Summary:

The histogram shows that the most common audit time is between 13 and 17 days, and the least common audit time is between 21 and 25 days.

Frequency, Cumulative Frequency, and Cumulative Percent Frequency Table:

The histogram shows that the most common audit time is between 13 and 17 days, and the least common audit time is between 21 and 25 days.

Frequency, Cumulative Frequency, and Cumulative Percent Frequency Table:

Year-end Audit Time (in Days)        Frequency        Cumulative Frequency        Cumulative Percent Frequency

13        3        3        15.00%

14        1        4        20.00%

15        1        5        25.00%

17        2        7        35.00%

19        1        8        40.00%

21        1        9        45.00%

22        1        10        50.00%

24        1        11        55.00%

25        1        12        60.00%

26        1        13        65.00%

27        1        14        70.00%

29        2        16        80.00%

30        1        17        85.00%

32        3        20        100.00%

b. Histogram Chart:

30  |                        

   |                        

   |                        

   |                        

25  |                        

   |             *          

   |             *          

   |             *          

20  |                        

   |             *          

   |             *          

   |             *          

15  |  *          *     *      

   |  *          *     *      

   |  *          *     *      

   |  *     *    *     *      

10  |  *     *    *     *      

   |  *     *    *     *      

   |  *     *    *     *      

   |  *     *    *     *      

   |------------------------

      13    17    21    25    29    33

In the histogram, the horizontal axis shows the range of values of the year-end audit time (in days), and the vertical axis shows the frequency. The asterisks (*) represent the frequency of each range. The histogram shows that the most common audit time is between 13 and 17 days, and the least common audit time is between 21 and 25 days.

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The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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Answer:

16

Step-by-step explanation:

x=16 because the Sides length and the degrees of the angle colide and show that x=16

Answer:

The Answer is 29cm

Step-by-step explanation:

The area of this shape is made from two shapes.

Shape one is a rectangle with the dimensions 2cm by 4cm

2x4 = 8

So the area of rectangle 1 is 8

The other rectangle has the dimensions 4cm by 7cm

Because you have to account for the other triangle not being there (solved)

4x7 = 21

21+8

29cm

The total energy value from these stated amounts is 214 calories.

To calculate the total energy value (in calories) from the stated amounts of protein, carbohydrates, fat, and alcohol, we can follow these steps:
1. Protein: Multiply the amount of protein (8 grams) by the energy value of protein (4 calories/gram).
2. Carbohydrates: Multiply the amount of carbohydrates (25 grams) by the energy value of carbohydrates (4 calories/gram).
3. Fat: Multiply the amount of fat (6 grams) by the energy value of fat (9 calories/gram).
4. Alcohol: Multiply the amount of alcohol (4 grams) by the energy value of alcohol (7 calories/gram).
5. Add the resulting values from steps 1-4 to find the total energy value (in calories).
Applying these steps:
1. Protein: 8 grams * 4 calories/gram = 32 calories
2. Carbohydrates: 25 grams * 4 calories/gram = 100 calories
3. Fat: 6 grams * 9 calories/gram = 54 calories
4. Alcohol: 4 grams * 7 calories/gram = 28 calories
5. Total energy value: 32 + 100 + 54 + 28 = 214 calories.

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Answer:

Step-by-step explanation:

p(x)=7x+20

p=7x/x + 20/x

answer   p=7+20/x

I hope its helpful.

Answer:

Draw the top and bottom line segments equal length and parallel. The perpendicular bisector of the lines are gonna be one line of symmetry. Next, draw the horizontal line of symmetry halfway between those. Pick two points on the horizontal line of symmetry that are symmetrical about the vertical line of symmetry. Connect those points to the ends of the top and bottom segments.

Step-by-step explanation:

(Images for more context)

Answer:

Step-by-step explanation:

Tanisha, Elicia, and Ajua are cousins. Tanisha is twice as old as Ajua, and Elicia is two years older than Tanisha. The sum of all their ages is 37. Use variable expressions and calculate the age of each girl

Let us represent:

The age of :

Tanisha = a

Elicia = b

Ajua = c

Tanisha, Elicia, and Ajua are cousins. Tanisha is twice as old as Ajua

a = 2c

c = 2/a

Elicia is two years older than Tanisha.l

b = a + 2

The sum of all their ages is 37.

a + b + c = 37

We substitute

a + a + 2 + 2/a = 37

2a + 2 + 2/a = 37

Use variable expressions and calculate the age of each girl

Answer:

V = 108

Step-by-step explanation:

B = 9 x 4 = 36 Height of Triangular prism is 3 so 36 x 3 = 108

Answer:

y = - 2x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x - 1 ← is in slope- intercept form

with slope m = - 2

• Parallel lines have equal slopes , then

y = - 2x + c ← is the partial equation of the parallel line

to find c substitute (4, 3 ) into the partial equation

3 = - 8 + c ⇒ c = 3 + 8 = 11

y = - 2x + 11 ← equation of parallel line