how many gallons of pure acid should be added to 480 gallons of 22% acid solution to produce a solution that is 36%?

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 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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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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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 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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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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yeah the nearest is porb 2.6 lol

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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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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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.

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 numbers are [tex]\sqrt[3]{-(89)}[/tex], [tex]-\sqrt{30}[/tex], [tex]15-\sqrt{2}[/tex], [tex]\sqrt[3]{43}[/tex], [tex]\sqrt{71}[/tex], 5.2, and 96 in that order.

To order the given numbers from least to greatest, we need to compare them to each other and arrange them in ascending order. Here's how we can do it:

Start with the smallest number: [tex]\sqrt[3]{-(89)}[/tex]. This is a negative number under the cube root, so it is the smallest among the given numbers.

Next, we have [tex]-\sqrt{30}[/tex]. This is a negative number, but its absolute value is smaller than that of [tex]\sqrt[3]{-(89)}[/tex]. So, it comes next.

After that, we have [tex]15-\sqrt{2}[/tex]. This is a number slightly greater than 13. It is greater than [tex]-\sqrt{30}[/tex] but less than [tex]\sqrt[3]{-(89)}[/tex].

The next number is [tex]\sqrt[3]{43}[/tex]. This is a number between 3 and 4, greater than [tex]-\sqrt{30}[/tex] and [tex]15-\sqrt{2}[/tex].

After that, we have [tex]\sqrt{71}[/tex]. This is a positive number, greater than 8 and less than 9.

Then we have 5.2. This is a number slightly greater than 5, greater than [tex]\sqrt{71}[/tex] and [tex]\sqrt[3]{43}[/tex].

Finally, we have the largest number: 96. This is clearly greater than all the other numbers.

Therefore, the order of the given numbers from least to greatest is:

[tex]\sqrt[3]{-(89)} , -\sqrt{30} , 15-\sqrt{2} , \sqrt[3]{43} , \sqrt{71}, 5.2, 96.[/tex]

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Answer:

refer the attachment

Step-by-step explanation:

your answers are

2√3 and 2

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.

The area of the polygon on the graph is 4 units²

The area of shape is the space enclosed within the perimeter or the boundary of a given shape. Area is measured in unit²

The polygon can be divided into two equal triangles by drawing a line through A to C. The area of the two triangles is then added together to give the area of the polygon.

area of triangle = 1/2 bh

= 1/2 × 2 × 2

= 2 units²

area of the polygon = 2+2

= 4 units²

therefore the area of the polygon is 4 units²

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Answer:

use pythagorean theorem on the lower tri to find its hypotenuse and apply the theorem again to find the base of the upper tri....

The rate at which the shadow of the man is increasing in length is 1/5 m/s.

We can solve this problem using similar triangles. Let x be the length of the shadow, and let y be the distance between the man and the base of the lamppost. Then, we have the following equation:

(1.4 + x)/y = 1/5

Solving for x, we get:

x = (y/5) - 1.4

Differentiating both sides with respect to time t, we get:

dx/dt = (1/5) dy/dt

We are given that dy/dt = 1 m/s, so substituting that in, we get:

dx/dt = (1/5) m/s

Finally, we are asked for the rate at which the shadow length is increasing, which is just dx/dt. Thus, the rate is (1/5) m/s.

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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: 29x +23

Step-by-step explanation: (2x + 4)(3x + 6) = 6[tex]x^{2}[/tex] + 24x + 24.

(3x - 1)(2x - 1) = 6[tex]x^{2}[/tex] - 5x + 1. 6[tex]x^{2}[/tex] + 24x + 24 - (6[tex]x^{2}[/tex] - 5x + 1) = 29x +23.

Required solutions after simplification are 8bz, 1, 3x³/y², 144, x⁹, 1/y⁵ respectively.

7) To simplify the expression:

[tex]\frac{16db {z}^{5} }{ {(2z)}^{4} } \\ = \frac{16}{2} \times \frac{b}{z} \times \frac{ {z}^{5} }{ {z}^{4} } \\ = 8b \times {z}^{5 - 4} \\ = 8bz[/tex]

Therefore, 16dbz⁵/(2z)⁴ simplifies to 8bz.

8)Any non-zero number raised to the power of zero is 1.

Therefore:(15n⁶m²x³/n⁻²m⁻³b⁻⁸)⁰ = 1

9)To simplify the expression:

[tex] \frac{30 {x}^{4} {y}^{ - 3} }{10 {x}^{ - 2} {y}^{5} }

= \frac{3 {x}^{4 - ( - 2)} }{ {y}^{3 - 5} }

= \frac{3 {x}^{6} }{ {y}^{ - 2} }

= \frac{3 {x}^{6} }{ {y}^{2} } [/tex]

herefore, 30x⁴y⁻³/10x⁻²y⁵

[tex]\frac{30 {x}^{4} {y}^{ - 3} }{10 {x}^{ - 2} {y}^{5} } [/tex] simplifies to [tex]\frac{3 {x}^{6} }{ {y}^{2} } [/tex]

13) To solve this expression, we perform the exponentiation first and then perform the multiplication.

6² means 6 multiplied by itself, or 6×6 = 36.

So,4×6² = 4×36

So, 4×6²= 144

Therefore, 4×6² equals 144.

14) To simplify the expression: x³ × x⁻² × x⁷ × x

[tex] = {x}^{3 - 2 + 7 + 1} = {x}^{9} [/tex]

Therefore, x³ * x⁻² * x⁷ * x simplifies to x⁹.

15)To simplify the expression:

[tex] {y}^{ - 11} \times {y}^{6} \times {y}^{0} \\ = {y}^{ - 11 + 6 + 0} \\ = {y}^{ - 5} \\ = \frac{1}{ {y}^{5} } [/tex]

Therefore, Required value is 1/y⁵.

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Answer:

2,444,444,442

Step-by-step explanation:

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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Option C. An ANOVA examines whether mean differences exist between conditions, whereas a t-test does not is the correct comparison between an ANOVA and a t-test.

What is ANOVA?

ANOVA (Analysis of Variance) is a statistical method that helps to compare three or more means or groups. It is used in behavioral and social sciences research, which determines whether the mean of the dependent variable is significantly different across different levels of an independent variable.

It is used for statistical inference in comparing the means of two or more groups. ANOVA is based on the idea of variance; that is, the variation between the groups' means is compared to the variation within the groups. By assessing the significance of the difference between group means, ANOVA determines whether there is sufficient evidence to conclude that they are not all equal.

What is a t-test?

A t-test is a statistical hypothesis test that compares the means of two independent groups. It is used when the data in each of the groups being compared is normally distributed. The t-test is a parametric test that compares the means of two groups and calculates the standard error of the difference between the means. It compares the difference between the two groups to the variability within each of the groups. The difference between the sample means is examined relative to the variability between the groups. The t-test produces a test statistic that can be compared to a critical value to determine if the means of the two groups differ significantly. It is commonly used to examine if the means of two independent groups are significantly different.

The primary differences between t-test and ANOVA are in terms of the number of groups, and that ANOVA is used for testing the significance of differences between more than two groups while t-tests are used for testing differences between two groups. Hence, ANOVA is used when we want to compare three or more groups, while t-tests are used when we want to compare two groups. Option C. An ANOVA examines whether mean differences exist between conditions, whereas a t-test does not is the correct comparison between an ANOVA and a t-test.

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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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Answer:

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

2nd and 4th

(10²)⁹=10¹⁸

10⁵/10¹⁵ = 10^-10

10⁷ × 10⁶ = 10¹³

you cant apply the laws of exponents where you have + or -