Using the quadratic formula, solve 0 = 2x² 2x² - 10x + 7 Give each of your answers to 2 d.p.​

Answer:

2,444,444,442

Step-by-step explanation:

Solution to the system of equations is (x, y) = (-7.933, 1.133) by elimination

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate the variable y by multiplying the second equation by 8 and adding it to the first equation.

Here are the steps to solve the system of equations:

Multiply the second equation by 8:

-2x - y = 17 --> -16x - 8y = 136

Add first equation to new equation:

x - 8y = -17 + (-16x - 8y = 136)

-15x = 119

Solve for x:

-15x = 119 --> x = -7.933 (rounded to three decimal places)

Substitute x into an original equation in order to solve for y:

x - 8y = -17 --> -7.933 - 8y = -17

-8y = -9.067

y = 1.133 (rounded to three decimal places)

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The probability that it will weigh between 687 grams and 825 grams is 90.47%

Using this formula, we can find the z-scores for the lower and upper bounds of the weight range we are interested in:

z₁ = (687 - 725) / 29 = -1.31

z₂ = (825 - 725) / 29 = 3.45

Next, we use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.

Using the table, we find that the probability of a standard normal distribution up to z₁ = -1.31 is 0.0951, and the probability up to z₂ = 3.45 is 0.9998. To find the probability between these two z-scores, we subtract the smaller probability from the larger one:

P(-1.31 < z < 3.45) = 0.9998 - 0.0951 = 0.9047

Therefore, the probability of picking a fruit that weighs between 687 grams and 825 grams is 0.9047, or 90.47% (rounded to 4 decimal places).

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The probability that the player has all 8 of the number selected by the lottery commission is approximately 1.3 × 10^-9.

There are a total of 40 numbers that can be chosen for the lottery. Out of those 40 numbers, a player must select 8 numbers. The lottery commission will also randomly select 8 numbers from those 40. If a player has all 8 of the numbers selected by the lottery commission, then they will win. The number of ways to choose 8 correct numbers is simply 1, since there is only one set of 8 numbers that the player can choose that matches the 8 numbers selected by the lottery commission.

The number of ways to choose any 8 numbers from 40 is given by the combination formula:

P = (40! / (8! (40 - 8)!) = 769,046,685

Therefore, the probability that the player has all 8 numbers selected by the lottery commission is:

P(all 8 numbers are correct) = 1 / 769,046,685 = 1.3 × 10^-9 (approximately).

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The IQ of students has a mean of 110 and an SD of 18. If 43 students are randomly sampled, the probability that the average IQ of this group is greater than 100 is P(Z > (100-110)/(18/√43)).

Given, that the IQ of students has a mean of 110 and SD of 18.

Number of students randomly sampled, n = 43.

The formula to calculate the probability is:

P(Z > (100-110)/(18/√43))

Now, substituting the values in the above formula:

P(Z > (100-110)/(18/√43))= P(Z > -2.365)= 1 - P(Z < -2.365)

This can be obtained by referring to standard normal tables or using a calculator.

Now, P(Z < -2.365) can be obtained by referring to standard normal tables or using a calculator.

Using a calculator, we get P(Z < -2.365) = 0.009 or 0.01 (rounded off to two decimal places).

So, P(Z > -2.365) = 1 - 0.01 = 0.99.

The probability that the average IQ of this group is greater than 100 is 0.99.

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Answer:

[tex] {(x - 3)}^{2} + {(y + 2)}^{2} = 4[/tex]

The capacity of the pyramid is 96000 cubic meters.

A pyramid is a three-dimensional geometric shape that consists of a polygonal base and triangular faces that meet at a common vertex, also known as the apex. Pyramids can have different shapes of base, such as square, rectangle, triangle, or any other polygon.

The capacity of a pyramid is given by the formula:

(1/3) x base area x height

The base of the pyramid is a square with side length 60 meters, so its area is:

base area = 60² = 3600 square meters

The height of the pyramid is 80 meters.

Therefore, the capacity of the pyramid is:

(1/3) x 3600 x 80 = 96000 cubic meters

So the capacity of the pyramid is 96000 cubic meters.

pyramids can be studied in terms of their surface area, volume, and other properties.

The volume of a pyramid can be found by using the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

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There is a building shaped like a square based pyramid. The length of each side of the building' base is 60 meters and the height of the building is 80 meters. What is the capacity of the pyramid?

The compound inequality that produced the given graph is x≤1 and y>2.Therefore the correct option is option (2) x≤1 and y>2.

A compound inequality is an inequality that contains two or more inequalities connected by either the word "and" or "or".

An "and" compound inequality is true only if both inequalities are true, while an "or" compound inequality is true if at least one of the inequalities is true.

The inequality x≤1 and y>2 represents the set of ordered pairs (x,y) that satisfy both conditions simultaneously.

Geometrically, this inequality represents the region in the coordinate plane that is below or on the vertical line x=1 and above the horizontal line y=2.

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The average number of bananas Jones's family eats is 11 bananas.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers.

To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

So, the average number of bananas the Jones family eats is:

We know that there are 52 weeks in a year. Then,

572/52 = 11

Therefore, the average number of bananas Jones's family eats is 11 bananas.

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In a group of 150 students, 20 are freshmen 30 are sophomores 49 are juniors and 51 are seniors if a student is randomly selected the probability that we select a sophomore before freshmen is 2.69%.

So the given data we get from the question is as follows,

  Total number of students, N = 150

  A number of freshmen students, F = 20

  The number of sophomore students, S = 30

  Number of junior students, J = 49

  Number of senior students, R = 51

              We need to find the probability of selecting a sophomore student before a freshman student. The probability that a sophomore student is selected first,

             P(S) = Number of sophomore students/Total number of students

                    = S/N

   Probability that a freshman student is selected after a sophomore student,

          P(F|S) = Number of freshman students left/Total number of students left

                    = F/N-1

    Where N-1 is used because one student has already been selected.

     The probability that a sophomore student is selected first and then a freshman student is selected,

       P(S∩F) = P(S) × P(F|S)

                   = S/N × F/N-1

      Therefore, the probability of selecting a sophomore student before a freshman student is:

       P(S∩F) = S/N × F/N-1P(S∩F)

                   = 30/150 × 20/149P(S∩

                   = 0.0269 or 2.69%

      Therefore, the probability of selecting a sophomore student before a freshman student is 0.0269 or 2.69%.

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The graph has three turns, which is an odd number, and it extends to a negative infinity.

What is the name of a polynomial graph?

A polynomial function's graph is essentially a continuous, smooth curve. You can use a few key features of this kind of graph to assist construct the curve. I'll explain how to use the polynomial function's leading term to analyze the graph's final performance.

If the number of turns is an odd integer, the functions have an even degree.

If the graph's behavior shifts to the negative infinity, the functional does have a negative leading coefficient.

Just this graph met the requirements among the options.

The graph has 3 turns (an odd number) and it goes to the negative infinity.

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The solution to this equation is x = -7 and x = 7.

The two numbers 7 units away from 0 on a number line are -7 and 7. This can be expressed mathematically as |x-0|=7, where x is the unknown number. Solving this equation yields two solutions, x = -7 and x = 7.

To solve this equation, first subtract 0 from both sides of the equation to get |x| = 7. Then, take the absolute value of both sides of the equation to get x = 7. Finally, note that the absolute value of any number is equal to that number's positive value. Therefore, the solution to this equation is x = -7 and x = 7.

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The value of the test statistic is -2.18.

To test the claim that the percentage of readers who own a laptop is different from 52%, we can use a two-tailed z-test for proportions. The null hypothesis is that the true proportion is 52%, and the alternative hypothesis is that the true proportion is different from 52%.

The test statistic can be calculated as:

z = (p - P) / sqrt(P(1 - P) / n)

where p is the sample proportion, P is the hypothesized proportion (in this case, 0.52), and n is the sample size.

Substituting the given values, we get:

z = (0.45 - 0.52) / sqrt(0.52(1 - 0.52) / 190)

z = -0.07 / 0.039

z = -1.79

The value of -1.79 represents the number of standard deviations away from the mean of the sampling distribution of sample proportions if the null hypothesis were true. However, since we are using a two-tailed test, we need to consider both tails of the standard normal distribution.

The critical value for a two-tailed test at the 0.05 level of significance is ±1.96. Since -1.79 is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, the correct answer is -2.18.

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The total number of valid numbers is 120= 108.

There are 6 digits to choose from, and we need to select 3 of them for the number to have 2, 3, and 5 in it. So, the total number of possible arrangements is 6P3 = 654 = 120.

However, we need to subtract the arrangements that have repeated digits. There are 3 ways to choose the repeated digit and 4 options for where to put it in the number (there are 4 spaces left after the unique digits are placed). This gives us 3*4 = 12 arrangements to subtract.

Therefore, the total number of valid numbers is 120 - 12 = 108.

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The sum of the angle measures of a polygon can be calculated using the formula (n - 2) × 180 degrees, where n is the number of sides. For a 31-gon, the sum of the angle measures is 5220 degrees.

To find the sum of the angle measures of a 31-gon, we can use the formula:

sum of angle measures = (n - 2) × 180 degrees

where n is the number of sides in the polygon.

Substituting n = 31 into the formula, we get:

sum of angle measures = (31 - 2) × 180 degrees

sum of angle measures = 29 × 180 degrees

sum of angle measures = 5220 degrees

Therefore, the sum of the angle measures of a 31-gon is 5220 degrees.

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Step-by-step explanation:

Start with point slope form for the line

point  5, 0

y - 0  = 6/5 ( x -5)

y = 6/5 x - 6     Done.

(a) The expressiοn that represents amοunt οf canned fοοd cοllected by  the three friends =  5x² + 5xy - 9

(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17

An expressiοn is a way οf writing a statement with mοre than twο variables οr numbers with οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Example: 2 + 3x + 4y = 7 is an expressiοn.

It is given that,

number οf cans cοllected by Jessa = 5xy + 17

number οf cans cοllected by Tyree = x²

number οf cans cοllected by Ben = 4x² - 8  

Part(a)

tοtal number οf cans cοllected by three friends = cans cοllected by Jessa + Tyree + Ben

= 5xy + 17 + x² + 4x² - 8

= 5x² + 5xy - 9

Part(b)

the gοal οf fοοd cans cοllected = 8x² − 4xy + 8

Sο, the number οf fοοd cans still left tο cοllect = gοal - (number οf cans cοllected)

= (8x² − 4xy + 8) - (5x² + 5xy - 9)

= 8x² - 5x² - 4xy − 5xy + 8 + 9

= 3x² - 9xy + 17

Therefοre,

(a) The expressiοn that represents amοunt οf canned fοοd cοllected by the three friends = 5x² + 5xy - 9

(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17

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When we can compare the simplified equation to the standard forms of the four main types of conic sections, we get that it has the form of an ellipse with its center at (3,6), a horizontal axis of length 2a = 4, and a vertical axis of length 2b = √(5/4)*4 = 2√5.

Circle: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius.

Ellipse: (x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center of the ellipse, a is the length of the horizontal axis, and b is the length of the vertical axis.

Parabola: y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a determines the direction and width of the parabolic curve.

Hyperbola: (x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center of the hyperbola. The distances between the center and each vertex on the horizontal axis and the vertical axis are denoted by the letters a and b, respectively.

The given equation is in the standard form of a conic section:

5(x − 3)² = 20 − 4(y − 6)²

To identify the type of conic section, we can simplify the equation by dividing both sides by 5:

(x − 3)² = 4 − (4/5)(y − 6)².

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Answer:

Step-by-step explanation:

-9+4.8=q-4.8+4.8

-4.2=q-4.8+4.8

-4.2=q

q=-4.2

The given number, 30, is in the sequence with a position of 6.

The given number, 90, is in the sequence with a position of 29.33.

Number is used to represent a quantity, such as an integer, fraction, or decimal.

The number is 30 and the nth term formula is 5n. To determine whether the given number is in the sequence, we need to solve for n.

Solving for n:

30 = 5n

n = 6

Therefore, the given number, 30, is in the sequence with a position of 6.

The number is 90 and the nth term formula is 3n + 2. To determine whether the given number is in the sequence, we need to solve for n.

Solving for n:

90 = 3n + 2

90 - 2 = 3n

88 = 3n

n = 29.33

Therefore, the given number, 90, is in the sequence with a position of 29.33.

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Answer:

x = 28*

Step-by-step explanation:

We know that Line M is parrallel to line N , so angle x = 28 degrees because the Alternate interior angles of a transversal are equal.

Hope it helps.

Answer:

1/2 of her beads are not red, and 3/4 of her beads are not green.

Step-by-step explanation:

If 1/2 of her beads are red, the other half can not be red, therefore meaning 1/2 of her beads are not red. If 1/4 if her beads are green, then the other 3/4 of her beads can not be green.

yeah the nearest is porb 2.6 lol

we can say that the teacher's gοal οf a standard deviatiοn οf at mοst 8 pοints was achieved, at a 5% level οf significance.

A measure οf a grοup οf values' variance οr dispersiοn in statistics is called the standard deviatiοn. When the standard deviatiοn is lοw, the values are mοre likely tο fall within a narrοw range, alsο knοwn as the expected value, whereas when the standard deviatiοn is high, the values tend tο be clοser tο the mean.

The lοwercase Greek letter sigma, which stands fοr the pοpulatiοn standard deviatiοn, οr the Latin letter s, which stands fοr the sample standard deviatiοn, are mοst frequently used in mathematical equatiοns and texts tο represent standard deviatiοn. Standard deviatiοn is alsο sοmetimes referred tο as SD.

suppοse that οn a 100-pοint test, the teacher's gοal is fοr her students' exam scοres tο have a standard deviatiοn οf at mοst 8 pοints.

chi²[tex]= (n-1)*s^2 /\sigma^2[/tex]

where n is the sample size, s is the sample standard deviatiοn, and sigma is the hypοthesized pοpulatiοn standard deviatiοn under the null hypοthesis.

In this case, n = 25, s = 9.5, and sigma = 8. Substituting these values, we get:

chi² [tex]= (25-1)*9.5^2 / 8^2 = 33.64[/tex]

The degrees οf freedοm fοr this test is n-1 = 24. Using a chi-squared table with 24 degrees οf freedοm, we find that the critical value fοr a οne-tailed test at a 5% level οf significance is 36.42.

Therefοre, we can say that the teacher's gοal οf a standard deviatiοn οf at mοst 8 pοints was achieved, at a 5% level οf significance.

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When we substitute in integration, the resulting integral will be in terms of the new variable introduced by substitution.

To understand about substitution in integration we need to have a clear idea about

Integration is a process of calculating the integral of a function. The integral of a function is the area under the curve of that function. There are various methods to integrate a function. Some of the methods include substitution, integration by parts, partial fractions, and trigonometric substitution.

Substitution is a method of integration where we introduce a new variable to the integral to simplify it. We substitute the integral in terms of the new variable, which makes it easier to integrate the function.

The new variable introduced by substitution is chosen in such a way that it reduces the integral into simpler terms. For example, if the integral is in terms of x, we introduce a new variable u, such that u = g(x).

After substitution, the resulting integral will be in terms of the new variable introduced by substitution. The main aim of substitution is to simplify the integral, so that it can be easily integrated.

Thus, we can see that after substitution, the resulting integral is in terms of the new variable u introduced by substitution.

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Answer:

refer the attachment

Step-by-step explanation:

your answers are

2√3 and 2

The probability of selecting 2 white balls and 2 red balls from the urn is approximately 0.412, which corresponds to option (d).

To solve this problem, we can use the hypergeometric distribution. The probability of selecting exactly k white balls and 4 - k red balls in a sample of 4 balls without replacement is given by:

P(k white balls) = [C(8,k) [tex]\times[/tex] C(10,4-k)] / C(18,4)

where C(n,r) is the number of combinations of n things taken r at a time.

For the given problem, we want to find the probability of selecting 2 white balls and 2 red balls, so we substitute k = 2 into the formula:

P(2 white balls) = [C(8,2) [tex]\times[/tex] C(10,2)] / C(18,4)

= [(28 [tex]\times[/tex] 45)] / 3060

≈ 0.412

Therefore, the probability of selecting 2 white balls and 2 red balls from the urn is approximately 0.412, which corresponds to option (d).

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