The area of a rectangular field is 8624 yd^2. If the length of the field is 98 yards, what is its width

Final answer:

The fourth rule of probability in statistics is the sum rule, which states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.

Explanation:

The fourth rule of probability in statistics is the sum rule. The sum rule is used when considering two mutually exclusive outcomes that can come about by more than one pathway. It states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.

For example, if we flip a penny (P) and a quarter (Q), the probability of getting one coin coming up heads and one coin coming up tails can be calculated as [(PH)  (QT)] + [(QH) × (PT)]

=( [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] ) + ( [tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] )

[tex]= \frac{1}{2}[/tex]

Answer:

4.9

Step-by-step explanation:

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:

It is D.x=4+√73

Step-by-step explanation:

Got it right on edg.2022 :))

The Circle's radius is roughly 3 kilometers.

To find the compass of a circle when given the circumference, we can use the formula

C = 2πr

where C is the circumference, and r is the compass.

Given that the circumference is18.84 kilometers, we can substitute these values into the formula and break for the compass

18.84 = 2 x3.14 x r

Dividing both sides of the equation by 2 x 3.14

18.84  /( 2 x 3.14) = r

Simplifying the right side

r ≈18.84/6.28

r ≈ 3 kilometers.

Thus, the circle's radius is roughly 3 kilometers.

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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:

[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]

Answer:

[tex]y=(x+4)^{2}-37[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

if a> 0 then the parabola open upward (vertex is a minimum)

if a< 0 then the parabola open downward (vertex is a maximum)

In this problem we have

[tex]y=x^{2}+8x-21[/tex]

Convert to vertex form

Complete the square

[tex]y+21=x^{2}+8x[/tex]

[tex]y+21+16=(x^{2}+8x+16)[/tex]

[tex]y+37=(x^{2}+8x+16)[/tex]

[tex]y+37=(x+4)^{2}[/tex]

[tex]y=(x+4)^{2}-37[/tex] --------> equation in vertex form

The vertex is the point [tex](-4,-37)[/tex]

the parabola open upward (vertex is a minimum)

Answer:

the answer is y=(x+4)^2-37

Step-by-step explanation:

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:

Since the bag contains 15 green, 18 yellow, and 16 orange balls, the total number of balls in the bag are 15+18+16=49.

Therefore, the probability of the event that the drawn ball is yellow is given by:

P(yellow)=[tex] \frac{Number of Yellow Balls}{Total Number of Balls} [/tex]

[tex] \therefore P(Yellow)=\frac{18}{49}\times 100\approx36.73\approx37 [/tex]%

Thus, the the probability of the event, to the nearest percent, that the drawn ball is yellow is 37%.

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.

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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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.