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3 months ago

You randomly survey students about year-round school. The results are shown in the graph.

Mathematics

1 answer:

AnnZ [12.3K]3 months ago

6 0

Answer:

27% and 37%

Step-by-step explanation:

The percentage of students against year-round schooling = 68%

The percentage of students in favor of year-round schooling = 32%

Margin of error = ± 5%

We need to create an equation with absolute values to determine the lower and upper limits of students supporting year-round schooling.

<pGiven that, the supporting percentage is 32% and the margin of error is 5%, this results in a variation of 5%, either adding or subtracting.<pThis can be expressed as:

| x - 32 | = 5

Where x signifies the lowest and highest percentages.

<pExpanding gives us:

x - 32 = -5 or x - 32 = 5

x = -5 + 32 or x = 5 + 32

x = 27% x= 37%

<pThis indicates that the smallest percentage of students who might support year-round schooling is 27%, while the maximum is 37%.

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A high school theater club has 40 students, of whom 6 are left-handed. Two students from the club will be selected at random, on

babunello [11817]

Response:

$1.92\%$

Detailed explanation:

Probability for an event is calculated as the ratio of the size of the event space compared to that of the sample space.

The sample space encompasses all possible outcomes.

Event space represents the number of favorable outcomes for the event in question.

Thus

Let

x ------> size of event space

y ----- → size of sample space

$P=\frac{x}{y}$

Calculate the probability of the first student being left-handed

we have

$x=6$

$y=40$

substituting values

$P=\frac{6}{40}$

Simplify

$P=\frac{3}{20}$

Calculate the probability of the second student being left-handed

we have

$x=6-1=5$

$y=40-1=39$

substituting values

$P=\frac{5}{39}$

Calculate the probability that both selected students will be left-handed

Multiply the probabilities together.

$P=\frac{3}{20}(\frac{5}{39})=\frac{15}{780}$

Convert to percentage

Multiply by 100

$\frac{15}{780}(100)=1.92\%$

4 0

3 months ago

Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retireme

Zina [12379]

Answer:

Kathy: $1,224,000

Mark: $306,000

Please refer to the attachment.

5 0

3 months ago

g A sailing ship stopped at several islands, releasing one mating pair of goats onto each one. On the large island, the goats' g

tester [12383]

Response:

The goat population will reach 1000 in a time span of 12.4 years

Detailed explanation:

After t years, the population of goats is described by

$N = N_0e^{bt}$

where $N_0$ indicates the initial count of goats and b is the growth rate per capita.

Based on the problem,

$N_0 = 2$
b = 0.5
N = 1000

$1000 = 2e^{0.5t}$

$e^{0.5t} = 500$

$0.5t = \ln 500 = 6.214$

$t = \dfrac{6.2}{0.5} = 12.4$

5 0

3 months ago

Read 2 more answers

If the area of the vegetable garden is 170 square feet which equation could be of use to find the length of the tomato patch? 0=

Svet_ta [12734]

Answer:

The equation 0 = 3x² + 17x - 160 might be useful in determining the length.

Step-by-step explanation:

The area of the vegetable garden is specified as 170 ft².

Now, regarding the provided equations;

1) For 0 = 3x² + 2x + 180, applying the quadratic formula results in:

x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)

x = [-2 ± √(-2151)]/6

The square root value is negative, indicating no real solution for x.

Thus, this equation does not help find the length.

2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.

3) For 0 = 3x² + 17x - 160, the roots when using the quadratic formula yield -10.67 or 5. The value 5 is viable since it is a whole number. Considering the area is also a whole number, this equation can be applied to ascertain the length.

4) For 0 = 3x² - 160, simplifying gives;

3x² = 160

x² = 160/3

x = ±√(160/3)

x = ±7.303

Since the area is a whole number but this length isn't, this equation may not accurately determine the length.

5 0

3 months ago

105,159 rounded to the nearest ten thousand

Svet_ta [12734]

In this problem the number we are working with is:

105,159

By definition we note:

thousand place: a five-digit quantity greater than zero.

Moreover, the rounding rule is:

if the digit being removed is 5 or more, increase the kept digit by one.

Therefore, rounding to the nearest ten thousand yields:

105,159 = 110,000

Answer:

105,159 rounded to the nearest ten thousand is:

105,159 = 110,000

6 0

3 months ago

Read 2 more answers