The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. the distribution of z-scores for those times is

Answer:

In probability, independent events are those that if one event occurs, it does not change the probability of the other event.

Whereas conditional probability is defined as the probability of one event occurring with some relationship to one or more other events.

The addition rule is used for both the independent and conditional probabilities.

For independent event the probability is shown as :

[tex]P(YorZ)=P(Y)+P(Z)[/tex]

For conditional: [tex]P(YorZ)=P(Y)+P(Z)-P(YandZ)[/tex]

To find the quotient of -7 ÷ 14/3, simplify the fraction 14/3 to 42/3 and then divide -7 by 42/3. The quotient is -1/2.

To find the quotient of -7 ÷ 14/3, we can simplify the fraction 14/3 to an improper fraction or a mixed number. Let's convert it to an improper fraction. We multiply the denominator (3) by the whole number (14) and add the numerator (0) to get the new numerator. This gives us 42/3. Next, we divide -7 by 42/3. When dividing by a fraction, we multiply by its reciprocal. So, -7 ÷ 42/3 is the same as -7 × 3/42. This simplifies to -21/42 which reduces to -1/2.

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Answer:

Different cities have different levels of sales tax for items purchased. Find each amount of sales tax?

What is 10% of $19.90?

$1.99

What is 7% of $20.00?

$1.40

Right on edge

Step-by-step explanation:

7 percent of the number 20.00 is 1.4.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given that, 7% of 20.00

A percentage is a number or ratio that can be expressed as a fraction of 100.

Let x be the 7% of 20.00.

Here, 7% of 20.00 =x

7/100 ×20.00 =x (word "of" means multiplication)

0.07×20.00 =x

x=1.4

Therefore, 7 percent of the number 20.00 is 1.4.

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24-7=17

17 pennies
7 nickles

total value is
5(7)+1(17)=35+17=52 cents

Vertically stretching the equation[tex]Y=x^3[/tex] by a factor of 4 results in the equation [tex]Y=4x^3[/tex]. This means that the value of the function increases four times for every x. Visually, the stretched function appears steeper along the y-axis.

The equation represents[tex]Y=x^3[/tex]   a cubic function. When you vertically stretch a function by a factor of 4, this means you multiply the output (Y-values) of the function by 4. Therefore, to vertically stretch Y=x3 by a factor of 4, you will multiply the entire function by 4. The final equation would look like [tex]Y=4x^3[/tex]

To clarify, the 'stretch' implies that for each x, the value of the function increases four times. This change can is noticeable graphically as the function will look 'steeper' or 'more stretched out' along the y-axis.

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Answer:

C = 5 over 9(F – 32)

Step-by-step explanation:

The formula is [tex]F=(\frac{9}{5}C)+32[/tex]

We can do some algebra to solve for C (note the steps below):

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

Last answer choice is right.

x = 71 degrees. Yes, the ladder meets safety standards.

A hypotenuse is defined as the longest side of a right triangle, the side opposite the right angle where the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of is the square of the lengths of the other two sides.

The equation is expressed as:

[tex]a^2 + b^2 = c^2[/tex]

a = side of right triangle

b = side of right triangle

c = hypotenuse

For above given information, the problem describes a right triangle with hypotenuse 12, the side against the ground is 4, and the angle between those two sides is "x".  

For this triangle,

cosx = (side adjacent to angle) / hypotenuse

   =  4 /12= 1/3

x  is approximately 70.52° which is 71° rounded to the nearest degree.

Thus, x = 71 degrees. Yes, the ladder meets safety standards.

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Final answer:

The solutions to ax = 0 are all vectors in the null space of the matrix a. These solutions can be expressed as a parametric vector form, which may involve free variables if the matrix a has any. The general solution is a linear combination of the basis vectors for this null space.

Explanation:

The question is asking to describe all solutions to the equation ax = 0 in parametric vector form, given that a is row equivalent to a certain matrix. This matrix is understood to allow a decomposition of a vector into its perpendicular components. Such a matrix transformation typically reduces to finding the null space of the matrix.

To find the solution to ax = 0, we understand that any vector x that satisfies this equation is in the null space of a. The null vector is the most trivial solution, where all components of the vector are zero. But if there are free variables involved, the solutions may form a subspace spanned by these free variables. The general solution can then be expressed as a linear combination of these basis vectors that span the null space of a.

For instance, if our matrix a has one free variable, the parametric vector form of the solution might be t[1,0,0] if the first column of a is the pivot column and the rest are free columns. Here, t would be any scalar, representing a line through the origin in the direction of the vector [1,0,0] in three-dimensional space.

Answer:

The first one :)

Step-by-step explanation:

Final answer:

To find the radius of a spherical tank with a capacity of 400 gallons, calculate the volume and use the formula for the volume of a sphere.

Explanation:

A spherical tank has a capacity of 400 gallons, which is approximately 533.47 ft³ (400 gallons x 0.1337 ft³/gallon).

To find the radius, use the formula for the volume of a sphere: V = (4/3)πr³. Set this equal to the volume and solve for the radius.

Substitute the volume (533.47 ft³) into the formula, solve for r, and you will find that the radius is approximately 4.88 feet.

The quotient of -18 and the sum of -2 and d can be represented mathematically as -18 ÷ (d - 2), where we subtract 2 from d and then divide -18 by that result.

The quotient of -18 and the sum of -2 and d refers to dividing -18 by the result of adding -2 to d (which we can represent as d - 2 because adding a negative number is equivalent to subtracting). Mathematically, we can express this as -18 ÷ (d - 2).

To perform this operation, we first need to know the value of d. Once we have that, we subtract 2 from it, and then divide -18 by that result.

For example, if d was 4, we would perform the operation as follows:  4 - 2 gives us 2, then -18 ÷ 2 gives us -9. So, the quotient of -18 and the sum of -2 and 4 (d being 4) is -9.

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The difference of the given fractions is 1/2.

Given that, 6/8 - 1/4.

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.

Here, 6/8 - 1/4

= 6/8 - 2/8

= (6-2)/8

= 4/8

= 1/2

Therefore, the difference of the given fractions is 1/2.

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To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. Apply the product rule and isolate dy/dx by moving terms.

To find dy/dx by implicit differentiation, we'll differentiate both sides of the equation with respect to x. Let's start by differentiating y cos x = 5x2 + 3y2:

Using the product rule, we have: dy/dx * cos x + y * (-sin x) = 10x + 6y * dy/dx

Next, isolate dy/dx by moving terms:

dy/dx * cos x - 6y * dy/dx = 10x - y * (-sin x)
dy/dx * (cos x - 6y) = 10x + y * sin x
dy/dx = (10x + y * sin x) / (cos x - 6y)

Answer: [tex]x^2+y^2=81[/tex]

Step-by-step explanation:

The equation of circle ( in general form ) is  given  by :_

[tex](x-h)^2+(y-k)^2=r^2[/tex]

, where r= radius of the circle .

(h,k) = center of the circle .

Given : Center = (h,k)= (0,0)

Radius = r = 9 units

Then the equation of the circle will be :-

[tex](x-0)^2+(y-0)^2=(9)^2[/tex]

[tex]\Rightarrow x^2+y^2=81[/tex]

Hence, the required equation of the circle  = [tex]x^2+y^2=81[/tex]

Final answer:

The equation of the vertical line passing through the point (14, 15) is x = 14.

Explanation:

To find an equation of a vertical line that passes through the point (14, 15), we need to understand that a vertical line has an undefined slope and therefore cannot be represented by the slope-intercept form of a line, y = mx + b. Instead, vertical lines are represented by equations where x is equal to a constant value since every point on the vertical line will share the same x-coordinate. Thus, the equation of the vertical line passing through (x, y) = (14, 15) is simply x = 14.

Answer:

D:3y+1

Step-by-step explanation:

find the Algebraic expression has a term with a coefficient of 3

The number before the variable is the coefficient

A:5y-7

y has a coefficient of 5

B:-2y+5+3

y has a coefficient of -2

C:3(y-6)

y or 1y are same

Here , y has a coefficient of 1

D:3y+1

y has a coefficient of 3