Clarence saved 19% of the money he earned. If Clarence earned $90, how much did he save?

Answer: Probability of getting a student in the school has head lice given that the test came back positive is 0.058.

Step-by-step explanation:

Since we have given that

Let E be the event that the student actually having head lice.

Let A be the event that the report shows positive.

Since there are 2% of the students in a school having lead lice.

P(E) = 0.02

P(E')=1-0.02=0.98

Similarly, the probability that the test for head lice is accurate = 75% of the time.

So, [tex]P(A\mid E)=75\%=0.75\\\\Similarly,\\\\P(A\mid E')=1-0.75=0.25[/tex]

We need to find the probability that a student in the school has head lice , given that the test came back positive.

So, By using Bayes Theorem, we get that

[tex]P(E\mid A)=\dfrac{P(A\mid E).P(E)}{P(A\mid E).P(E)+P(A\mid E').P(E')}\\\\P(E\mid A)=\dfrac{0.02\times 0.75}{0.02\times 0.75+0.98\times 0.25}\\\\P(E\mid A)=\dfrac{0.015}{0.015+0.245}\\\\P(E\mid A)=\dfrac{0.015}{0.26}\\\\P(E\mid A)=0.0576\approx 0.058=5.8\%[/tex]

Hence, Probability of getting a student in the school has head lice given that the test came back positive is 0.058.

For the given system of equations, the value of k determines the number of real number solutions.

In order to determine the number of real number solutions for the system of equations y = x^2 and y = x + k, we need to analyze the discriminant of the quadractic equation x^2 - (x + k) = 0.

The discriminant of the quadratic equation x^2 - (x + k) = 0 can be calculated as b^2 - 4ac, where a = 1, b = -1, and c = -k.

For no real number solutions: b^2 - 4ac < 0

For one real number solution: b^2 - 4ac = 0

For two real number solutions: b^2 - 4ac > 0

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Since Wanda's height represents 100% and Will is 23% taller, then Will's height is 123% of Wanda's height.

The question tells us that Will is 23% taller than Wanda. In terms of understanding this percentage in relation to Wanda's height, it helps to see Wanda's height as 100% because 100% represents a whole, in this case, Wanda's entire height. If Will is 23% taller, then his height is 100% of Wanda's plus an additional 23%. Thus, Will's height is 123% of Wanda's height.

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Answer:

NO. They do not have to be equal

Step-by-step explanation:

A whole number takes place when two conditions are satisfied:

1. The numerator or the dividend is greater than the divisor.

  For example, when you divide 0.1 by 0.002.

  The dividend 0.1 is greater than 0.002

2. The divisor is small than the dividend.

   This rule is the same as one above.

    for example:

   the quotient x is given by [tex]\frac{1}{0.25}\\ = 4[/tex]

Final answer:

The area of a kitchen measuring 3.75 meters by 4.2 meters is calculated by multiplying these dimensions, resulting in an area of 15.75 square meters.

Explanation:

The question asks for the area of a kitchen with dimensions 3.75 meters by 4.2 meters. To find the area of a rectangle, you multiply its length by its width. Therefore, the calculation for the area of the kitchen is as follows:

Area = Length × Width= 3.75 m × 4.2 m

= 15.75 square meters

Thus, the area of the kitchen is 15.75 square meters. This calculation is a basic application of geometry, specifically dealing with areas of rectangles.

I would have to say it would be D. On average, city A was warmer than city B.

Hope this helps ;}

Answer:False

Step-by-step explanation:

The correct answer is 33 days. The least number of days until Camryn practices both the flute and trumpet again is 33 days.

To determine how many days until Camryn practices both the flute and trumpet again, we need to find the least common multiple (LCM) of the two periods: every 11th day for the trumpet and every 3rd day for the flute.

The LCM of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 11 and 3, we can list the multiples of each number until we find a common multiple:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, ...

Multiples of 11: 11, 22, 33, ...

The smallest common multiple of 3 and 11 is 33. Therefore, Camryn will practice both instruments again in 33 days.

Alternatively, we can calculate the LCM using the prime factorization of the two numbers. Since 3 is a prime number and 11 is also a prime number, the LCM is simply the product of the two:

LCM(3, 11) = 3*11 = 33

Thus, the least number of days until Camryn practices both the flute and trumpet again is 33 days.

Final answer:

The expression ax²-ay-bx²+cy+by-cx² can be factored by first combining like terms to get (a-b-c)x² + (b+c)y - ay and then refactoring to x²(a-b-c) + y(b+c-a).

Explanation:

The student has given the expression ax²-ay-bx²+cy+by-cx² to factor. To factor this expression, we must first combine like terms and then group the terms in a way that allows us to factor by grouping.

Combining like terms gives us: (a-b-c)x² + (b+c)y - ay. We can then factor out common factors from each group. Notice that x² terms can be grouped together, as well as the y terms.

The refactored expression is x²(a-b-c) + y(b+c-a). Depending on the specific values of a, b, and c, further factoring may be possible, but with the given information, this is the factored form of the expression.

Final answer:

To factor the expression ax² - ay - bx² + cy + by - cx², group the terms based on their factors and factor out the common factors. The factored form of the expression is x²(a - b - c) - y(a - c + b).

Explanation:

To factor the expression ax² - ay - bx² + cy + by - cx², we can group the terms based on their factors. Group ax² - bx² - cx² together, and -ay + cy + by together. Factoring out the common factors from each group, we get:

x²a - b - c) - y(a - c + b)

Thus, the factored form of the expression is x²(a - b - c) - y(a - c + b).

I believe the answer would be 0.5

Hope this helps ;}

Answer: The correct answer is (B) 0.5.

Step-by-step explanation:  Given that A(5, 3) , B(3, 7)  and C(1, 4) are the vertices of ΔABC and  A′(2.5, 1.5) , B′(1.5, 3.5) and C′(0.5, 2) are the vertices of ΔA'B'C'.

We are to find the scale factor of the dilation of the centre of dilation is origin.

We know that the scale factor of dilation is given by the following formula:

[tex]S_c=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]

We can calculate the lengths of the corresponding sides AB and A'B' of ΔABC and ΔA'B'C' respectively using distance formula as follows:

[tex]AB=\sqrt{(3-5)^2+(7-3)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt5,\\\\A'B'=\sqrt{(1.5-2.5)^2+(3.5-1.5)^2}=\sqrt{1+4}=\sqrt{5}.[/tex]

Therefore, the scale factor for the dilation is given by

[tex]S_c=\dfrac{A'B'}{AB}=\dfrac{\sqrt5}{2\sqrt5}=\dfrac{1}{2}=0.5.[/tex]

Thus, the required scale factor is (B) 0.5.

A story problem for the division problem is: 5 friends sharing going on a holiday and the total cost is $32

From the question, we have the following parameters that can be used in our computation:

32 divided by 5

Also, we have the result to be

Result = 6 2/5

A story problem for this division is as follows:

Five friends decided to go on a holiday together. After calculating the total cost of $32, they split it evenly, so each friend contributed $6 2/5.

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Please find the attached file for a better understanding of the solution provided here:

ABCD is the swimming pool and PQRS is the extent of the swimming pool plus the concrete walkway which is 6 yards wide.

Now, we know that the length is 8 yards shorter than twice it's width. Thus,

l=2w-8

Now the area of the region, A'B'QP will be: length x width. Now, the length here is l+6+6=2w-8+12=2w+4 and width is 6.

Thus, area of the region A'B'QP is (2w+4)x6=12w+24

Likewise, the area of the region D'C'RS will similarly be 12w+24 too.

Now, the area of the region BB'C'C will be 6 x w=6w

Similarly, the area of the region AA'D'D will be 6 x w=6w

Therefore, the total area of the walk way will be:

[tex] 2(12w+24)+2\times 6w=570 [/tex]

[tex] 24w+48+12w=570 [/tex]

[tex] 36w+48=570 [/tex]

[tex] \therefore w=14.5 [/tex]

Therefore, length, l will be:

[tex] l=2w-8=2\times 14.5-8=29-8=21 [/tex]

Therefore, the dimensions of the swimming pool are:

Length, l= 21 yards and Width, w=14.5 yards