Let z be a standard normal variable. Find the value of z if z satisfies p( -z < z < z) = 0. 8788.

On solving the provided question, we can say that value of the equation , h = \(\frac{M}{Zg} + f\)

Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.

here,

the equation

\(Z=\frac{M}{g(h-f)}\)

\(for, h , \\h - f = \frac{M}{(Zg)}\\h = \frac{M}{Zg} + f\)

value of the h will be \(\frac{M}{Zg} + f\)

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Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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Answer:

x =62     y=118

Step-by-step explanation:

The sum of two opposite angles in a cyclic quadrilateral is equal to 180 degrees (supplementary angles)

x+44+74= 180

x+118=180

x=62

      y-48+110=180

     y+62=180

      y=118

Answer:

its ln 4, A as seen in the image.  

I might be wrong sry?

Answer:

C. 49

Step-by-step explanation:

Side a = 9.89949 = 7√2

Side b = 14

Side c = 9.89949 = 7√2

1/2 x 7√2 x 7√2 = 49

Hope this helps :)

The amount of soil needed to cover the garden is 49 sq.ft, the correct option is C.

According to Pythagoras Theorem, in a right angled triangle the square of the side opposite to the right angle is equal to the sum of squares of the other two sides.

Height² + Base² = Hypotenuse²

The right triangle has hypotenuse of 14ft  

As the other two angles are eqaul

The base and height of the triangle will be equal

Let the base and height of the triangle is x ft

By Pythagoras theorem,

x² +x²= 14²

2x² = 196

x² = 98

x = 9.9 ft

The area of the triangle will be equal to needed to cover the garden with a layer of soil

The area of the triangle is = (1/2) * base * height

Area of the triangle = (1/2) * 9.9 * 9.9

Area of the triangle is 49 sq.ft

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The circumcenter of triangle ABC is (-5, 2)

What is the circumcenter?

The circumcenter of a triangle is the point that is equidistant from all three vertices of the triangle. It is the center of the circle that passes through all three vertices of the triangle.

To find the circumcenter of the triangle ABC with vertices A(-5,3), B(5, 8), C(-5.8) we can substitute the values of the coordinates into the formulas above:

x = (8 - 3) * (-5.8^2 + 3^2 - 5^2 - 8^2) - (3 - 8) * (-5^2 + 3^2 - (-5)^2 -3^2) / 2 * (3 - (-5)) * (8 - 3) - (3 - 8) * (-5.8 - (-5))

x = (-5)

y = (3 - (-5.8)) * (-5^2 + 3^2 - (-5)^2 -3^2) - (-5 - (-5)) * (3^2 + 3^2 - (-5.8)^2 - 8^2) / 2 * (3 - 8) * (-5 - (-5)) - (3 - 8) * (3 - (-5.8))

y = 2

Hence, the circumcenter of triangle ABC is (-5, 2)

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Answer:

(0, 5.5)

Step-by-step explanation:

Midpoint of BC: ([-5 + 5]/2, (8 + 8)/2) = (0, 8)

Perpendicular bisector of BC has equation: x = 0

Midpoint of AC: ([-5 + (-5)]/2, (3 + 8)/2) = (-5, 5.5)

Perpendicular bisector of AC has equation y = 5.5

Point of intersection of the two perpendicular bisectors:

(0, 5.5)

Answer: (0, 5.5)

Answer:

y-intercept : 3

x-intercepts are 1 and 2

Vertex is at (2,-1)

Axis of symmetry is at x = 2

Step-by-step explanation:

See attached graph.

The equation y = x² – 4x + 3 represents a parabola

y-intercept at is at B(0,3); y-intercept is 3

x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3

The vertex is the lowest point on this parabola (2-1)

Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 2

Answer:

a  c  e

Step-by-step explanation:

Answer:

206.428km/hr

Step-by-step explanation:

a train travels 1445/2km in7/2 hr

the speed of the train in km/hr

=1445/2km/7/2 hr=(1445×2)/(2×7)=206.428km/hr

A scatter plot or a line graph could be used to represent the relationship between the two variables.

A scatter plot is a graph in which each data point is represented by a dot on the graph. In this case, the data points would represent the amount of money spent on groceries and the percentage of that money spent on fruits and vegetables. Each data point would be plotted based on its corresponding values for the two variables, with the horizontal axis representing the amount of money spent on groceries and the vertical axis representing the percentage of that money spent on fruits and vegetables. The scatter plot would allow us to see if there is any relationship between the two variables, such as whether people who spend more on groceries tend to spend a higher percentage of that money on fruits and vegetables.

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Answer:1) 1661

Step-by-step explanation:23x23 =529, 529xpi=1661

Answer:

Step-by-step explanation:

Answer:

6 is in the tens place

Step-by-step explanation:

5 is is the hundreds place. 6 is in the tens place and 8 is in the ones place.

\(*GraceRosalia*\\*IAmAnExpertICanHelpYou*\\PleaseMarkBrainliestThankYou\)

Applying the rules for the constant, logarithm and exponents, the derivative of the given function is of:

f'(x) = 3/x - 6x² - 8/(x^5).

The function is given by:

f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4

The derivative of a sum is the sum of the derivatives, hence:

f'(x) = (√2^3)' + (ln(x^3))' - (2x^3)' - (log_3(729))' - (2/x^4)'

The derivative of a constant is of zero, hence:

Hence:

f'(x) = (ln(x^3))' - (2x^3)' - (2/x^4)'.

The derivative of the logarithm is given by:

ln(h(x))' = (1/h(x)) x h'(x).

Hence:

(ln(x^3))' = 3x²/x³ = 3/x.

The derivative of the power of x is given by:

[x^n]' = nx^(n-1).

Hence:

Hence the derivative of the function is given by:

f'(x) = 3/x - 6x² - 8/(x^5).

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The maximum volume of the prism is 1728 cubic centimeters.

To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.

Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.

First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.

By using the Pythagorean theorem, we can find 'a':

a^2 + a^2 = 24^2

2a^2 = 576

a^2 = 288

a = √288

Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.

Therefore, the dimensions of the prism for maximum volume are:

Base length (a) = √288 cm

Height (h) = 12 cm

To find the maximum volume, we can use the formula for the volume of a right triangular prism:

Volume = (1/2) * a^2 * h

Substituting the values, we get:

Volume = (1/2) * (√288)^2 * 12

= (1/2) * 288 * 12

= 1728

Hence, the maximum volume of the prism is 1728 cubic centimeters.

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\(y = (1/5) x^5 + Ce^ {(-x^5)}\) is the general solution of the given differential equation.

The given differential equation is:

y' + 5x⁴ y = x⁴

To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is \(e^{(int 5x^4 dx)}\):

\(e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}\)

The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is \(e^{(x^5)}\):

\(e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)\)

Now we can recognize the left-hand side as the product of the derivative of the product of \(e^{(x^5)\)and y:

\((d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}\)

Integrating both sides with respect to x, we get:

\(e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C\)

where C is the constant of integration. Dividing both sides by \(e^{(x^5)}\), we get the general solution:

\(y = (1/5) x^5 + Ce^(-x^5)\)

where C is an arbitrary constant.

\(y = (1/5) x^5 + Ce^{(-x^5)}\) is the general solution of the given differential equation.

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Answer:

$0.39

Step-by-step explanation:

First find the unit rate for store B ( $8.84/13)

At store B Artuto spends $0.68 for one bottle of apple juice

At store A they spent $0.29

0.68-0.29= 0.39

Answer:

$6.35

Step-by-step explanation:

10 quarters =

10 × .25 = $2.50

17 dimes =

17 × .10 = $1.70

40 nickels =

40 × .05 = $2.00

15 pennies =

15 × .01 = $0.15

2.50+1.70+2.00+.15

= 6.35

The total is $6.35.

The total perimeter will be 4x^+17 and length be 22.76 cm

As per the data given in the questions,

We have, the shape of the sandwich be rectangular.

We know that, perimeter of the rectangle can be determined by using formula: 2(l+b),

where, l = length of the rectangle

and, b = breadth of the rectangle

The expression for the perimeter of the sandwich would be:

2 (2x^2 + 9) + 2 (2x^2 + 8)

= 4x^2 + 26

Now for finding the length of the crust,

we will put the value of x=1.2,

So, the value of the approximate length of the crust would be:

=4x^2 + 26

= 4 * 1.2^2 + 26

= 22.76 centimetres.

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Answer:

See below.

Step-by-step explanation:

There is nothing to solve without some additional information. Does the problem state what is to be done, or does it contain any information on the values of x or y? For example:

1) Rearrange for x:

y= x-2

x = y+2

2) What is the value of x if y is 3?

y= x-2

(3)= x-2

x = 5

Answer: look at explanation <3

Step-by-step explanation:

Steps to find the equation of a line from two points:

Find the slope using the slope formula

Use the slope and one of the points to solve for the y-intercept (b).

One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

 Mid point of a segment divides the segment in two equal parts.

Value of x is 3.

  It's given in the question,

Therefore, EF = FG = (6x + 7)

And EF + FG = EG (By segment addition postulate)

Now substitute the values in the expression

(6x + 7) + (6x + 7) = (18x - 4)

12x + 14 = 18x - 4

12x - 18x = -14 - 4

-6x = -18

x = 3

            Therefore, the value of x is 3.

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Answer:

4 + 4 = 8

Step-by-step explanation:

The new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

The correct equation to find the new tuition for the fall is: B. 1.15 • 3500 = x

Here's why: The problem states that there is a 15% increase in tuition, which means that the new tuition will be the current tuition plus 15% of the current tuition. Mathematically, we can represent this as:

new tuition = current tuition + 15% of current tuition

Using x to represent the new tuition, and 3500 to represent the current tuition, we can write this equation as:

x = 3500 + 0.15(3500)

Simplifying the right side, we get:

x = 3500 + 525

x = 4025

Therefore, the new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

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The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

The given equation represents the motion of a mass connected to a spring with viscous friction. To plot the displacement, y(t), we need to solve the differential equation. With initial conditions y(0) = 0, we can find the solution using the Laplace transform. After solving the equation, we can plot y(t) for t < 0 and t ≥ 0 separately. For t < 0, the applied force, f(t), is zero, so the mass will not experience any external force and will remain at rest. For t ≥ 0, the applied force is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position.

To solve the given differential equation, we can start by finding the characteristic equation by setting the coefficients of y, its derivative, and its second derivative to zero:

s^2 + 18s + 102 = 0.

Solving this quadratic equation gives us the roots s1 = -3 + 3i and s2 = -3 - 3i. These complex roots indicate that the mass will undergo damped oscillations.

Using the Laplace transform, we can solve the differential equation and obtain the expression for Y(s), the Laplace transform of y(t):

(s^2 + 18s + 102)Y(s) = F(s),

where F(s) is the Laplace transform of f(t). Since f(t) = 10 for t ≥ 0, its Laplace transform is F(s) = 10/s.

Solving for Y(s) gives us:

Y(s) = 10 / [(s^2 + 18s + 102)].

To find y(t), we need to inverse Laplace transform Y(s). Using partial fraction decomposition, we can express Y(s) as:

Y(s) = A / (s - s1) + B / (s - s2),

where A and B are constants to be determined. After finding A and B, we can inverse Laplace transform Y(s) to obtain y(t).

With the given initial condition y(0) = 0, we can solve for A and B by setting up equations using the initial value theorem:

A / (s1 - s1) + B / (s1 - s2) = 0,

A / (s2 - s1) + B / (s2 - s2) = 0.

Solving these equations will give us the values of A and B. Finally, we can substitute these values back into the inverse Laplace transform of Y(s) to obtain y(t).

For t < 0, since the applied force f(t) is zero, the mass will not experience any external force. Therefore, y(t) will remain at its initial position, y(0) = 0.

For t ≥ 0, the applied force f(t) is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position. The displacement, y(t), will depend on the properties of the mass, the spring, and the viscous friction. The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

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Answer:

7980

Step-by-step explanation:

Answer:

The correct answer is 1/2×8×3.

The output obtained after executing the java code snippet,

double bottles;

double bottleVolume = bottles * 2;

System.out.printIn(bottleVolume);

will throw an error that bottle variable might not have been initialized.

As per the question statement, we are provided with a java code snippet, which goes as:

double bottles;

double bottleVolume = bottles * 2;

System.out.printIn(bottleVolume);

We are required to determine the output, that we will obtain on executing the above mentioned code.

That is, on executing the code

double bottles;

double bottleVolume = bottles * 2;

System.out.printIn(bottleVolume);

We will obtain an error that bottle variable might not have been initialized because we are using the variable bottle without initializing.

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Answer:

8.4

Step-by-step explanation:

9-3/5

=9/1 - 3/5 (nothing in denominator means there is one)

=(9×5-3)/5 (taking L.C.M)

=(45-3)/5

=42/5

=8.4

When you square both sides of an equation, the occurrence of extraneous roots is not directly linked to the presence of an x^2-term. Therefore, option b. false is correct.

When you square both sides of an equation, you may introduce extraneous roots, but this is not directly related to the presence of an x^2-term. The occurrence of extraneous roots depends on the specific manipulations performed during the equation solving process, such as applying non-invertible operations.

Squaring both sides of an equation can lead to extraneous roots when the equation contains radicals or fractional exponents. For example, consider the equation √x = 2. Squaring both sides gives x = 4, which is a valid solution. However, squaring introduces an extraneous root because when you substitute x = 4 back into the original equation, you get √4 = 2, which is true, but it does not satisfy the initial equation. In this case, the extraneous root is x = 16.

In contrast, the presence of an x^2-term does not inherently cause extraneous roots. Squaring both sides of an equation with an x^2-term can be a valid operation as long as it is applied correctly. The resulting equation may have real or complex solutions, but they won't be extraneous purely because of the x^2-term.

When you square both sides of an equation, the occurrence of extraneous roots is not directly linked to the presence of an x^2-term. Extraneous roots can appear due to the specific manipulations involved in the equation solving process, such as squaring both sides when there are radicals or fractional exponents.

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