Prove or disprove: for all integers a, b, c, if a|bc, then a|b or a|c.

In a standard normal distribution, the probability of getting a positive number is 0.5.

Probability of Getting a Positive Number in a Standard Normal Distribution

In a standard normal distribution, the probability of getting a positive number is 0.5. This is because the standard normal distribution is symmetric around 0, and half of the distribution lies to the right of 0, which corresponds to positive numbers.

To solve the expression 12 + 3 • 8, first perform the multiplication to get 24, then add this to 12 to get a final result of 36.

To evaluate the expression 12 + 3 • 8, you must follow the order of operations, often remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. As per PEMDAS, multiplication should be carried out before addition.

First, perform the multiplication: 3 times 8 is 24. Then, add the result to 12.

So, 12 + 24 equals 36. Therefore, the value of the expression 12 + 3 • 8 is 36.

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Answer:

the answer is C.

Step-by-step explanation:

83%

The true statement about the given conditional Probability is; The probability that event A occurs, given that event B occurs, is 83%.

We are told that If events A and B are independent, and the probability that event A occurs is 83%.

Now, Conditional probability like p(A|B) is the probability of event A occurring, given that event B occurs. Thus, applying that to our question means we can denote that;

The probability that event A occurs, given that event B occurs, is 83%.

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Answer:

B. 10.44 units.

Step-by-step explanation:

We are asked to find the length of line segment AB.

To find the length of line segment AB we will use distance formula.

[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Upon substituting the coordinates of point A and B in distance formula we will get,

[tex]\text{Distance between point A and point B}=\sqrt{(1--9)^2+(-1--4)^2}[/tex]

[tex]\text{Distance between point A and point B}=\sqrt{(1+9)^2+(-1+4)^2}[/tex]

[tex]\text{Distance between point A and point B}=\sqrt{(10)^2+(3)^2}[/tex]

[tex]\text{Distance between point A and point B}=\sqrt{100+9}[/tex]

[tex]\text{Distance between point A and point B}=\sqrt{109}[/tex]

[tex]\text{Distance between point A and point B}=10.4403065089105502\approx 10.44[/tex]

Therefore, the length of line segment AB is 10.44 units and option B is the correct choice.

Answer:

I'm a nooby so 10.44.

Step-by-step explanation:

Answer:

The answer is Z equals negative 3/2

Step-by-step explanation:

Final answer:

The perimeter of the polygon, given the sides (2x + 1), (4x – 10), (x + 1), and (12x + 25), is calculated by summing these expressions to get 19x + 17.

Explanation:

To find the perimeter of a four-sided polygon, we add together the lengths of all the sides. Given the sides (2x + 1), (4x – 10), (x + 1), and (12x + 25), the perimeter P in terms of x is calculated by summing these expressions:

P = (2x + 1) + (4x – 10) + (x + 1) + (12x + 25)

Now, we combine like terms:

P = 2x + 4x + x + 12x + 1 – 10 + 1 + 25

P = (2x + 4x + x + 12x) + (1 – 10 + 1 + 25)

P = 19x + 17

Therefore, the perimeter of the polygon in terms of x is 19x + 17.

The ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

For this case, we're specified that:

Then, the area of the circle is:

[tex]\pi r^2 \: \rm unit^2[/tex]

and the area of the square is: [tex]\rm side^2 = (2r)^2= 4r^2 \: \rm unit^2[/tex]

The ratio of the area of the circle to the area of the square is:

[tex]\dfrac{\pi r^2}{4r^2} = \dfrac{\pi}{4} = \pi : 4[/tex]

Thus, the ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4

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Answer:

It is D.x=4+√73

Step-by-step explanation:

Got it right on edg.2022 :))

First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. In total, she earned $72. Therefore:

8 ( 4 + x ) = 72

( 4 + x ) = 72 / 8

4 + x = 9

x = 9 - 4

x = 5

Leticia babysat 5 hours on Saturday.

Answer:

No, because it doesn't satisfy the equation of the circumference

Step-by-step explanation:

A circle is the locus of points on the plane that are equidistant from a fixed point called the center.  For a circle whose center is the point

[tex]C=(a,b)[/tex]

and its radius is [tex]r[/tex], the ordinary equation of this circle is given by:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

Since the circle is centered at the origin:

[tex]C=(a,b)=(0,0)\\\\Hence\\\\(x-0)^2+(y-0)^2=r^2\\\\x^2+y^2=r^2[/tex]

Now, let's find [tex]r[/tex] using the data provided. Evaluating the point (0,-4) into the equation:

[tex](0)^2+(-4)^2=r^2\\\\16=r^2\\\\r=\pm 4[/tex]

Thus the equation for the circle given by the problem is:

[tex]x^2+y^2=16[/tex]

In order to corroborate if the the point (2 3, 2) lie on the circle, we need to evaluate it into the equation and check if it satisfy the equation:

Note: I don't know what you mean with 2 3, so I will assume 3 cases:

[tex]2\hspace{3} 3=23\\2\hspace{3} 3=2*3=6\\2\hspace{3} 3=\frac{2}{3}[/tex]

First case:

[tex](23)^2+(2)^2=16\\\\533\neq16[/tex]

It doesn't satisfy the equation, therefore doesn't lie on the circle.

Second case:

[tex](6)^2+(2)^2=16\\\\40\neq16[/tex]

It doesn't satisfy the equation, therefore doesn't lie on the circle.

Third case:

[tex](\frac{2}{3} )^2+(2)^2=16\\\\\frac{40}{9} \neq16[/tex]

It doesn't satisfy the equation, therefore doesn't lie on the circle.

Final answer:

The point (3, 2) does not lie on the circle centered at the origin with a radius of 4 units because when its coordinates are plugged into the circle's equation x² + y² = 16, the result is not equal to the radius squared.

Explanation:

To determine if the point (3, 2) lies on the circle centered at the origin that contains the point (0, -4), we need to see if it satisfies the equation of the circle.

We know the radius of the circle is the distance from the center to the point (0, -4), which is 4 units since all points on a circle are equidistant from the center.

The general equation for a circle centered at the origin (0,0) is x² + y² = r², where r is the radius.

Our circle's equation is x² + y² = 16.

We plug in the coordinates of the point (3, 2) to see if it lies on the circle: 3² + 2² = 9 + 4 = 13, which is not equal to 16. Therefore, the point (3, 2) does not lie on the given circle.

Answer:

C. Linearly, because the table shows that temperature increased by the same amount each month

Step-by-step explanation:

We have been given the expression [tex] (a^8)^4 [/tex].

To solve this problem we will use one of the rules of the exponents called the Power Rule.

The power rule states that:

[tex] (x^m)^n=x^{m\times n}=x^{mn} [/tex]

In our case, x=a and the powers involved are m=8 and n=4.

Therefore, applying the power rule to the case given in our question we get:

[tex] (a^8)^4=a^{8\times 4}=a^{32} [/tex].

Therefore, Option D which says [tex] \boldsymbol{a^{32}} [/tex] is the correct option.

Answer:

4(base*height)/2

Answer:

[tex]y=2x^2[/tex]

B is correct

Step-by-step explanation:

Given: We are given equation of parabola ans to choose narrowest graph.

[tex]y=ax^2[/tex]

Parabola form narrowest and widest.

Larger value of a most narrowest graph.

Smaller value of a most widest graph.

Now, we will see the coefficient of x²

[tex]y=\dfrac{1}{6}x^2,\ \ \ a=\dfrac{1}{6}[/tex]

[tex]y=2x^2,\ \ \ a=2[/tex]

[tex]y=-x^2,\ \ \ a=-1[/tex]

[tex]y=\dfrac{1}{8}x^2,\ \ \ a=\dfrac{1}{8}[/tex]

Now, we arrange the value of a in descending order.

[tex]2>1>\dfrac{1}{6}>\dfrac{1}{8}[/tex]

2 is largest value of these.

Hence, The narrowest graph is [tex]y=2x^2[/tex]

The 15 days it takes for 8 goats and 8 cows to eat 17 acres of grass if it takes 2 goats and 3 cows 6 days to eat 2 acres of grass. it takes 6 goats and 5 cows 10 days to eat 8 acres of grass.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

it takes 2 goats and 3 cows 6 days to eat 2 acres of grass. it takes 6 goats and 5 cows 10 days to eat 8 acres of grass.

Number of days to eat 2 acres for  2 goats and 3 cows = 2/6

Number of days to eat 8 acres for 6 goats and 5 cows = 8/10

Now adding the fraction number of 2/6 and 8/10

[tex]\rm = \frac{2}{6}+ \frac{8}{10}[/tex]

= 68/60

= 15/17

Now the number of days is 15 days for the 17 acres.

Thus, the 15 days it takes for 8 goats and 8 cows to eat 17 acres of grass if it takes 2 goats and 3 cows 6 days to eat 2 acres of grass. it takes 6 goats and 5 cows 10 days to eat 8 acres of grass.

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Answer:

4.9

Step-by-step explanation: