A survey found that 60% of shoppers at My-Way-Store like chocolate ice cream. If 240 boppers like chocolate ice cream, how many people were surveyed?

Answer:

x = 3

angle B = 70 degree

angle C = 50 degree

Step-by-step explanation:

angle B + angle C = angle CDA ( exterior angle property)

(22x+4) + (15x +5) = 120

22x + 15x + 4 + 5 = 120

37x + 9 = 120

37x = 120- 9

37x = 111

x = \(\frac{111}{37}\)

x = 3

angle B = 22x + 4

            = 22(3) +4

            = 66 +4

angle B = 70 degree

angle C = 15x+5

             = 15( 3) + 5

             = 45 + 5

angle C = 50 degree

Hope this helps.

Answer:

0.023 meters

Step-by-step explanation:

We know 1000 mm is equal to 1m so:

\(23mm \times \frac{1m}{1000mm} = 0.023m\)

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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The values of f(1), f(2), f(3), and f(4) for the function f(x) = 0.2x + 0.7 are:

f(1) = 0.9

f(2) = 1.1

f(3) = 1.3

f(4) = 1.5

To find the values of f(1), f(2), f(3), and f(4) for the function f(x) = 0.2x + 0.7, we simply substitute the given x-values into the function and evaluate.

f(1):

Substitute x = 1 into the function:

f(1) = 0.2(1) + 0.7

= 0.2 + 0.7

= 0.9

f(2):

Substitute x = 2 into the function:

f(2) = 0.2(2) + 0.7

= 0.4 + 0.7

= 1.1

f(3):

Substitute x = 3 into the function:

f(3) = 0.2(3) + 0.7

= 0.6 + 0.7

= 1.3

f(4):

Substitute x = 4 into the function:

f(4) = 0.2(4) + 0.7

= 0.8 + 0.7

= 1.5

Therefore, the values of f(1), f(2), f(3), and f(4) for the function f(x) = 0.2x + 0.7 are:

f(1) = 0.9

f(2) = 1.1

f(3) = 1.3

f(4) = 1.5

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Answer:

I am odd number my digits add up to 7 i am bigger than 50 and smaller 100

Answer:

The measure of angle 2 equals the measure of angle 7 by the alternate angles theorem

\(\huge\text{Hey there!}\)

\(\large\boxed{\mathsf{b - \dfrac{a}{8}}}\\\\\\\large\boxed{\mathsf{= 44 - \dfrac{48}{8}}}\\\\\\\large\boxed{\mathsf{= \dfrac{44}{1} - \dfrac{48}{8}}}\\\\\\\large\boxed{\mathsf{= \dfrac{44}{1} - \dfrac{6}{1}}}\\\\\\\large\boxed{\mathsf{= \dfrac{44 - 6}{1}}}\\\\\\\large\boxed{\mathsf{44 - 6 = \bf 38}}\\\\\\\large\boxed{\mathsf{= 38\div 1}}\\\\\\\large\boxed{= \mathsf{38}}\\\\\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{38}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\large\boxed{\heartsuit\ \frak{Amphitrite1040:)\ \star}}\)

we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

To calculate the p-value, we need to perform a hypothesis test.

Let's assume the null hypothesis is that the proportion of defective systems produced by x-game is equal to or less than the industry standard of 0.02, while the alternative hypothesis is that the proportion is greater than 0.02.

We can use the normal approximation to the binomial distribution since we have a large sample size (n=120) and np and n(1-p) are both greater than or equal to 10.

The test statistic can be calculated as:

\(z = (p_hat - p) / \sqrt{(p*(1-p)/n)}\)

where \(p_hat\)  is the sample proportion of defective systems, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Using the values given in the question, we have:

\(p_hat = 6/120 = 0.05\)

p = 0.02

n = 120

Plugging these values into the formula, we get:

\(z = (0.05 - 0.02) / \sqrt{(0.02*(1-0.02)/120) = 2.041}\)

The p-value can be calculated as the probability of getting a test statistic as extreme or more extreme than 2.041 under the null hypothesis.

Since this is a one-tailed test (the alternative hypothesis is one-sided), we look up the area in the right tail of the standard normal distribution table.

Using a standard normal distribution table, we find that the area to the right of 2.041 is 0.0207.

Therefore, the p-value is 0.0207.

Therefore, we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

This means that there is strong evidence that the proportion of defective systems produced by x-game exceeds the industry standard of 0.02.

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Answer:

x=2

Step-by-step explanation:

After solving with substitution, you would know x = 2

Step-by-step explanation:

\(\textsf{\large{\underline{Solution}:}}\)

→ 5x - 2y = 6 ----- (i)

→ 3x + 2y = 10 ---- (ii)

Adding (i) and (ii), we get:

→ 8x = 16

→ x = 16/8

→ x = 2

Substituting the value of x in (i), we get:

→ 5 × 2 - 2y = 6

→ -2y = 6 - 10

→ -2y = -4

→ y = -4/-2

→ y = 2

Therefore:

→ (x, y) = (2, 2) (Answer)

\(\textsf{\large{\underline{Verification}:}}\)

Put x = 2 and y = 2 in second equation, the LHS becomes:

= 5 × 2 - 2 × 2

= 10 - 4

= 6

= RHS

Put x = 2 and y = 2 in second equation, the LHS becomes:

= 3 × 2 + 2 × 2

= 6 + 4

= 10

= RHS

Hence, our answer is correct (Verified)

Hope this helps!!

Answer:

\(a) \left(4c-a\right)\times\left(4c+a\right)\)

\(=\left(4c\right)^2-a^2\)

\(=16c^2-a^2\)

-------------------

\(b) (4x-3)\times(6x+1)\)

\(=4x\times \:6x+4x\times \:1+\left(-3\right)\times \:6x+\left(-3\right)\times \:1\)

\(=4\times \:6xx+4\times \:1\times \:x-3\times \:6x-3\times \:1\)

\(=24x^2-14x-3\)

-------------------

\(c)(x-y)\times(x^2+5y)\)

\(xx^2+x\times \:5y+\left(-y\right)x^2+\left(-y\right)\times \:5y\)

\(=x^2x+5xy-x^2y-5yy\)

\(=x^3+5xy-x^2y-5y^2\)

OAmalOHopeO

Answer:

first

Step-by-step explanation:

half of right angle

The cost of 5 pairs of shoes is 108.78 dollars.

The cost of 3 pairs of shoes is $65.27. At this price, the cost of 5 pairs of shoes can be calculated as follows:

Let's find the cost of each pair of shoes before we can get the cost of 5 pairs of shoes.

Therefore,

3 pairs of shoe = 65.27 dollars

1 pair of shoes = ?

cross multiply

cost of each pair = 65.27 / 3

cost of each pair = 21.76 dollars

Therefore, the cost of 5 pairs of shoes can be found as follows:

cost of 5 pairs of shoes = 21.76 × 5

cost of 5 pairs of shoes = 108.783333333

Therefore,

cost of 5 pairs of shoes = 108.78 dollars

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There is no graph provided for reference, but if the graph shows a probability distribution, then the probabilities that are equal to 0.3 would depend on the specific shape and values displayed on the graph.

Without this information, it is impossible to determine which probabilities are equal to 0.3. Based on the given information, the graph represents a probability distribution. To determine which probabilities are equal to 0.3, you would need to analyze the graph (which is not provided). However, I can explain each term:
1. p(5≤x≤8): This represents the probability that x falls between 5 and 8, inclusive.
2. p(x≤3): This denotes the probability that x is less than or equal to 3.
3. p(x≥3): This signifies the probability that x is greater than or equal to 3.
4. p(3≤x≤5): This indicates the probability that x falls between 3 and 5, inclusive.

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For the function ƒ(x) = px + q, the values of ƒ(0), ƒ(1), ƒ(5), and ƒ(-2) can be determined. They are: (a) ƒ(0) = q, (b) ƒ(1) = p + q, (c) ƒ(5) = 5p + q, and (d) ƒ(-2) = -2p + q.

The function ƒ(x) = px + q represents a linear function with a slope of p and a y-intercept of q. Evaluating the function for different values of x gives us the corresponding y-values.

(a) When x = 0, we have ƒ(0) = p(0) + q = q. Therefore, ƒ(0) is equal to the y-intercept q.

(b) For ƒ(1), we substitute x = 1 into the function: ƒ(1) = p(1) + q = p + q.

(c) Similarly, for ƒ(5), we have ƒ(5) = p(5) + q = 5p + q.

(d) Finally, for ƒ(-2), we substitute x = -2 into the function: ƒ(-2) = p(-2) + q = -2p + q.

Therefore, the values of ƒ(0), ƒ(1), ƒ(5), and ƒ(-2) are q, p + q, 5p + q, and -2p + q, respectively.

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Answer:

To find (f•g)(-2), we need to first calculate f(-2) and g(-2).

f(-2)=-3(-2)-1=-7

g(-2)=(-2)^2+5=9

Then, we can calculate (f•g)(-2) as follows:

(f•g)(-2)=f(-2)g(-2)=-7*9=-63

Yes, it can be concluded at a 0.01 level of significance that there is a linear correlation between the two variables.

The following is a solution to the given question. The weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling is given by the data. The correlation coefficient between the two variables is to be tested to conclude if there is a linear correlation between the two variables at a 0.01 level of significance.

Linear correlation between the two variables A correlation coefficient, r, is used to determine if two variables have a linear correlation. A value of r=1 indicates a perfect positive correlation, while a value of r=-1 indicates a perfect negative correlation. A value of r=0 indicates no correlation between the two variables.To find the correlation coefficient, we use the following formula:

\($r = \frac{n\sum xy - \sum x\sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$\)

Where

Weight, \($x$\)  Rolling Distance \($y$59 2683 4397 4956 20103 6587 4488 4891 4252 3963 3371 39100 4989 55103 5399 4274 3375 3089 30102 40103 3399 3386 3785 37\)

We need to find n,

\($\sum x$\) \($\sum y$\) \($\sum x^2$\)\($\sum y^2$\)

\(\sum xy$.n=30$\\ \sum x=2792$$\\ \sum y=1129$$\\ \sum x^2=221506$$\\ \sum y^2=86223$$\\ \sum xy=106883$r = 0.91\)

Correct to two decimal places.

Decision RuleWe have to check if the value of r lies in the critical region for a 0.01 level of significance. The value of r that separates the critical region from the non-critical region is found using the following formula:

\($$r_c = \frac{1}{\sqrt{n-2}}$$\)

Where n is the sample size.

Substituting the values, we get

\($$r_c = \frac{1}{\sqrt{30-2}} = 0.366$$\)

The critical region is when r is greater than 0.366 or less than -0.366.

Conclusion The value of r (0.91) is greater than the critical value (0.366). Hence, we conclude that there is a linear correlation between the two variables at a 0.01 level of significance. Therefore, the answer is: Yes, it can be concluded at a 0.01 level of significance that there is a linear correlation between the two variables.

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A sample size of 669 is required to be 99% confident that the estimate of the percentage of people with headaches who prefer this particular brand of painkiller is within 2 percentage points.

To determine the sample size required to estimate the percentage of people with headaches who prefer a particular brand of painkiller with a 99% confidence level and a margin of error of 2 percentage points, we can use the formula for sample size calculation for proportions.

The formula is given by:

\(n = (Z^2 * p * (1 - p)) / E^2\)

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, for a 99% confidence level, Z = 2.576)

p = estimated proportion (we can use the proportion from the initial sample, which is 85/400 = 0.2125)

E = margin of error (0.02 or 2 percentage points)

Substituting the values into the formula:

\(n = (2.576^2 * 0.2125 * (1 - 0.2125)) / 0.02^2\)

Calculating the expression:

n = 668.34

Rounding up to the nearest whole number, the required sample size is 669.

Therefore, a sample size of 669 is required to be 99% confident that the estimate of the percentage of people with headaches who prefer this particular brand of painkiller is within 2 percentage points.

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Answer:

146.5 sq cm

Step-by-step explanation:

48.5 +24.5x4

24.5 times 4 = 98

98 + 48.5 = 146.5

Answer: 25

Step-by-step explanation: I just entered the equation into my calculator like so.

A negative number times a negative number equals a positive number.

I hope this helps, have a nice day.

The answer satisfies the definition of a function because for every input (sales revenue), there is a unique output (weekly income). The appropriate domain for this function is all possible values of sales revenue, represented as [0, ∞) in interval notation.

Let's define the variable x as the weekly sales revenue. The salesperson's weekly income can be calculated by adding their fixed salary of $800 to the commission earned, which is 4% of the sales revenue.

The equation for the weekly income (y) in terms of the sales revenue (x) is y = 0.04x + 800, where 0.04 represents 4% as a decimal.

This equation satisfies the definition of a function because for every possible value of sales revenue (x), there is a unique corresponding value of weekly income (y). In other words, each input has exactly one output.

The domain of this function represents all possible values for the sales revenue. Since there is no restriction on the sales revenue, the appropriate domain is [0, ∞), indicating that the sales revenue can range from 0 to infinity. The left bracket [ indicates that the function includes 0 as a possible value, and the infinity symbol ∞ indicates that there is no upper bound for the sales revenue.

Therefore, the weekly income function satisfies the definition of a function, and its appropriate domain is [0, ∞) in interval notation.

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Answer:

28/10

Step-by-step explanation:

To find out scale factor, you need to divide both sides which means

7/2.5 is 2.8 and if we turn that into a fraction we get 28/10

Jane lost 5 points in the game.

Given that, Jane gained 25 points in the first round of a game. In the second round, she lost 40 points and in the third round, she gained 10 points.

We need to write and evaluate an expression to find how many points Jane gained or lost.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Now, for the given situation we can write an expression as follows:

25 – 40 + 10

=25 + 10 + ( -40 )

=35 -40= -5

Therefore, Jane lost 5 points in the game.

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Answer:

Step-by-step explanation:

The area of the square is 3 units by 3 units. because the area of a square is side length squared.

side length = 3

side length^2 = 3 * 3 = 9

The area of a circle is much harder to reason out. You could start with the area of a square and use the diameter is 3 units. But the corners are rounded and you don't know off hand what the area of one of them is, let alone all 4. You are given a formula for circles area, but you have no real idea what the formula actually means. Does it take the corner area into account? At the beginning levels, we don't know.

Answer:

The area of the square is 9 aka \(3^{2}\)

You can find it easily by just counting the number of squares inside the square, or by counting the number of squares at its length then multiplying it by its width; so 3 x 3 = 9

It wouldn't be as easy to find the area of the circle because you don't have the radius, nor diameter, so basically, no quantitative values could be used to at least guess.

First graph is the correct one.

when x= 1

y=f(x) = -√1 = -1

when x= 2

y= -√2

Answer:

it should be A

Holly is correct.

Step-by-step explanation:

The value of z at 99.2% confidence is 2.41 in the proportion of population.

To find the value of z at a specific confidence level, we need to use a standard normal distribution table or a calculator that can perform normal distribution calculations.

The z-value corresponding to a 99.2% confidence level can be found by looking up the area of 0.996 (which is 1 - 0.008, where 0.008 is half of the 0.016 area corresponding to the tail probability beyond the z-value) in the standard normal distribution table or using a calculator in the interval. Using a standard normal distribution table, we can find that the z-value corresponding to an area of 0.996 is approximately 2.41. Therefore, the answer is 2.41.

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Answer:

Sorry i don't know the answer but which class question is this

The fraction of people were born in France is 7/24 .

What is a Pie Chart?

A pie chart is a graphical representation used to describe the composition of a data using degrees or percentages.

Given,

The pie chart represents the results when 120 people in a shopping centre were asked which country they were born in.

So, from the given pie chart

105° is given as the number of people that were born in the France

That's about: 105/360 × 120 = 35 people.

35 out of 120 people would give us a fraction of: 35/120 = 7/24 .

Hence, The fraction of people were born in France is 7/24 .

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Answer:

The answer is B. In step one he should have added 3 negative x-tiles to both sides.

See attachment for complete question.

Answer:

The correct option is B.

In step one he should have added 3 negative x-tiles to both sides.

Step-by-step explanation:

Given the equation

3x + 1 = 4x + (-4)

Adding 3 negative x tiles, we have

3x + 1 + (-3x) = 4x + (-4) + (-3x)

1 = x - 4

x = 1 + 4 = 5