A school staff meeting had 60 teachers in attendance, 30% of whom were first-year teachers. How many first-year teachers were in the meeting?

Answer:

it'll look like the last one -7x + 2 = 16

The average speed in miles per hour during her drive that morning is 43.5 miles per hour   .

In the question ,

it is given that ,

the distance between home to freeway entrance is = 0.6 miles

the distance between freeway entrance to freeway exit is = 15.4 miles

the distance between freeway exit to workplace is = 1.4 miles

So , the distance from home to work place = 0.6 + 15.4 + 1.4 = 17.4 miles

we know that 24 minutes = 24/60 = 0.4 hours ,

the average speed = total  distance / total time

= 17.4/0.4

= 43.5 miles per hour

Therefore , the average speed is 43.5 miles per hour .

The given question is incomplete , the complete question is

One morning, Ms. Simon drove directly from her home to her workplace in 24 minutes. what was her average speed, in miles per hour, during her drive that morning ?

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Using system of linear inequality, the number of tacos and burrito he sold was 56 and 54 respectively

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

To solve this problem, we have to write two system of inequality and then graph the inequalities to show the solution.

Let;

x + y = 110 ...eq(i)

7x + 3.25y ≥ 560 ..eq(ii)

From eq(i)

x + y  110

x = 110 - y ..eq(iii)

Put eq(iii) into eq(ii)

7(110 - y) + 3.25y ≥ 560

770 - 7y + 3.25y ≥ 560

770 - 3.75y ≥ 560

-3.75y ≥ 560 - 770

-3.75y ≥ -210

y ≤ 56

Assuming y is less than or equal to 56, x will be

x + 56 = 110

x = 54

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The money invested in stock X is $8,800.

Given,

Total investment in stock portfolio=$10000

Expected return from stock X=13%=0.13

Expected return from stock Y=8%=0.08

Expected return from portfolio=12.4%=0.124

The portfolio return is calculated by taking the weighted average of individual stock returns.

Let x represent the portfolio weightage of stock X.

1-x is the portfolio weightage of stock Y.

money invested in stock X be

0.124=0.13x+0.08(1-x)

0.124=0.13x+0.08-0.08x

0.124-0.08=0.05x

0.044=0.05x

x=0.88

money invested in stock X=0.88*10000=$8800

Thus, the money invested in stock X is $8,800.

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The average birthweight of a nonsmoker was between 1,000 and 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.

Given,

What is the newborn's weight?

A newborn's body weight is referred to as birth weight. At birth, babies of European descent typically weigh between 2.5 and 4.5 kilograms, or about 3.5 kilograms on average. South Asian and Chinese babies typically weigh 3.26 kg.

Here,

Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.

However, there are some obvious disparities between the two groups' typical ranges of birth weights. Since there are fewer newborns in the lower weight groups, over half of neonates among nonsmokers (56 out of 115, 48.7%) had birth weights between 3,000 and 4,000 grams. Less infants are born in the heavier weight categories; 40 of the 74 newborns delivered to smokers, or 54% of them, had birth weights between 2,000 and 3,000 grams.

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In total 6 weeks, the saved money by both Sadio and Thoma will be in the ratio of 2:1.

For the given question.

Initial money owned by each is-

Sadio = $15

Thoma = $0.

Let the number of weeks passed be 'x'.

Then, present money after x weeks.

Sadio = $3.50x + 15

Thoma = $3x

The number of weeks , when ratio becomes 2:1

(3.50x + 15)/3x = 2/1

3.50x + 15 = 6x

6x - 3.5x = 15

x = 15/2.5

x = 6

Thus, in total 6 weeks, the money held by both Sadio and Thoma will be in the ratio of 2:1.

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Graph D is a function because it passes the vertical line test

A vertical line test helps to find if the graph is a function or not. The vertical line in a coordinate system represents a set of infinite points having the same x coordinate values and different y coordinate values for each of its points. The vertical line is drawn parallel to the y-axis, if it cuts the curve at one distinct point then it has one y-value for the given x value and it follows the basic definition of a function.

Applying the vertical line test in the graphs given, only graph D is a function.

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Answer:

(0,2)

Step-by-step explanation:

plug in 0 for x

a) To factorize this expression, we need to find two numbers that multiply to give 8 and add to give 6. The two numbers that fit this description are 4 and 2, so we can write the expression as x² + 6x + 8 = (x + 4)(x + 2).

b) To factorize this expression, we need to find two numbers that multiply to give 18 and add to give -9. The two numbers that fit this description are -6 and -3, so we can write the expression as x²-9x + 18 = (x - 6)(x - 3).

c) To factorize this expression, we need to find two numbers that multiply to give -9 and add to give -8. The two numbers that fit this description are -3 and 3, so we can write the expression as x² - 8x-9 = (x - 3)(x + 3).

d) To factorize this expression, we need to find two numbers that multiply to give -27 and add to give 6. The two numbers that fit this description are -9 and 3, so we can write the expression as x² + 6x-27 = (x + 9)(x - 3).

The value of x on the boundary line and the x axis is found as 4.

For the given question,

The graph of inequality  x-2y ≤ 4 is drawn.

Consider the graph,

The straight lien formed by the graph touches the x coordinate axis at (4,0).

Thus, the value of x on the boundary line and the x axis is found as 4.

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The line segment has a length of 13 units. (Correct choice: D)

According to Euclidean geometry, any line can be constructed by the locations of two distinct points on Cartesian plane. In this question we must determine the length of the line segment by means of Pythagorean theorem, whose formula is shown below:

l = √(x² + y²)

Where:

First, determine the horizontal and vertical lengths of the line segment:

x = 12, y = 5

Second, determine the length of the line segment:

l = √(12² + 5²)

l = √169

l = 13

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The approximate percentage training hours are delivered online is 30%

What is percentage ?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.

10%, a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. (Value/Total Value)100% is the formula used to calculate percentages.

The amount of hours remitted online are 25.6% in 2018 reports

It has reduced from last year , it has been reported 28.6% in 2017 and 30.4% in 2016

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Answer: A

Step-by-step explanation:

4y=5x-16

divide each side by 4

y=5/4x-4

Answer:

Step-by-step explanation:

5/4 is the answer

cause you add =4y to other side and -16 to left side

divide by 4 on both sides to get

5/4x -4 = y

The probability that the shipment will be accepted anyway is 0.0885.

Given,

In the question:

A random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that 8% of the apples on the truck do not meet the desired standard.

To find the probability that the shipment will be accepted anyway.

Now, According to the question:

The sample size, n = 150.

The population proportion, p = 0.08.

The shipment is accepted of the sample proportion is less than 5%.

Now, to find the required probability the listed conditions to verified.

Randomization: It was stated that a random sample is chosen.

Independence: It can be supposed that the fact that a sample is satisfactory is independent of the other apple's condition.

10% condition: It can be supposed that the population size is larger than 150 (sample size).

Normality: This condition requires that np and n (1 − p) must be at least 10, so it can be verified as,

np = (150 x 0.08)

np = 12 [tex]\geq[/tex] 10

The mean of the sample proportion can be estimated as:

μ[tex]_p[/tex] = p

    = 0.08

Similarly, The standard deviation of the sample proportion can be estimated as:

σ[tex]_p[/tex] = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

    =  [tex]\sqrt{\frac{0.08(1-0.08)}{150} }[/tex]

    =  0.02215

Thus, the sampling distribution of sample proportion can be approximated as,

p ~ N(0.08 ~ 0.0222)

The required probability is given as:

P(p < 0.05) = P (p - μ[tex]_p[/tex] /σ[tex]_p[/tex]  < 0.05 - 0.08/ 0.0222)

                  = P(Z < -1.35)

                 = 1 - P (Z < 1.35)

                  = 0.0885

Note: The probability value corresponding to the Z score is obtained from the unit normal table.

Thus, the probability that the shipment will be accepted anyway is 0.0885.

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Marko needs the amount of money which would be $20 to go to a concert.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have been given that Marko has $22. He needs at least $42 to go to a concert.

We have to determine the required amount of money Marko

the required amount of money = cost of the concert - he has the amount

the required amount of money = $42 - $22

Apply the subtraction operation, and we get

the required amount of money = $20

Therefore, Marko needs the amount of money that would be $20.

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Answer:

170 Degrees.

Step-by-step explanation:

If an interior angle is 170 degrees, that's your best bet.

Answer:

85baskets

Step-by-step explanation:

17*5=85 baskets,if each basket hold 5kickballs 17*5.

The slope value of the linear relationship tells us how much Austin pays to his friend weekly, which is: $8.

A linear relationship between two variables, x and y, can be defined by the equation, y = mx + b, where the value of m is the slope and b is the y-intercept or starting value.

If we have a table that represents a linear relationship between two variables, x and y, what we need to do is to use two pairs of values from the table to find the change in y / change in x.

In this context, L = amount Austin owes his friend for t weeks, so the slope will be the amount Austin pays to his friend every week = change in L / change in t.

Using two pair of values from the table, (1, 32) and (4, 8):

Slope (m) = change in L / change in t = (32 - 8) / (1 - 4)

Slope (m) = 24/-3

m = -8

Therefore, the amount Austin will be paying to his friend weekly would be $8.

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Answer:

84

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let, the dimension of cuboid are l=5x,b=4x and h=2x

Now, the surface area of cuboid =2(5x×4x+4x×2x+2x×5x)=76x2

Now,

76x2=1216

x2=16

x=4

Dimensions of cuboid are,

l=5x=5×4=20cm,b=4x=4×4=16cm

h=2x=2×4=8cm

Volume of cuboid=l×b×h=20×16×8=2560cm3

Hence, this is the answer.

The dimension of the rectangle of maximum area that you can enclose with the string is 12.5 x 12.5

n let x = the length of one side of the rectangle and y = the length of the other side of the rectangle.

The area is:

A = xy

and the perimetere is the string of length 50 cm

50 = 2(x + y) Solve this in terms of y. Divide both sides by 2.

25 = x + y By Subtract x from both sides.

25-x = y Now substitute this into the equation for the area.

A = x (25 - x) Simplify.

A = 25x - x²

the general form of quadratic equation: ax² + bx + c

x is given by -b/2a

Here the equation is A = -x² + 25x

, a = -1, b = 25, and c = 0

so we can find the x-coordinate of the vertex by -25/2(-1) = 12.5

So the length (x) of the rectangle must be 12.5 cm to get the maximum area.

But what about the width (y)?

Since the perimeter is 50 cm and this is twice the (length + width), the (length + width) is 25 cm, so the width is 25 cm - the length.

x + y = 25

12.5 + y = 25

y = 12.5

So, we end up with x (the length) = 12.5 cm and y (the width) = 12.5 cm.

And this, of course, is a square whose sides are 12.5 cm

If the perimeter were k cm,

2(x + y) = k

x + y = k/2

x + x = k/2 (as x = y)

x = k/4

x = k/4, y = k/4

Therefore,  the dimension of the rectangle of maximum area that you can enclose with the string is 12.5 x 12.5

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A normal distribution can appear utterly erratic due to a lack of data. Results from tests taken in class, for instance, are often regularly distributed.

Given information;

Scores from the sit and reach test weren't normally distributed.

To find what is the likely cause for this lack of normal distribution,

⇒ A normal distribution can appear utterly dispersed due to Insufficient Data. For instance, test scores in the classroom are often regularly distributed.

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Answer:

Step-by-step explanation:

1. x=5

2. xy7

Answer:

Step-by-step explanation:

Correct option is A)

Using combinations, we know that 4 different types of items will be selected.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

We can choose the components of combos in any order.

Permutations and combinations can be mixed up.

Combination formula: [tex]n C r=\frac{n !}{(n-r) ! r !}[/tex]

So, this formula, commonly known as the NCR formula, determines the number of combinations that may be made with r items out of the n available options.

We, therefore, have 4 objects, and a person chooses 3 at random.

[tex]\begin{aligned}& n C r=(n, r)=(4,3) \\& =\frac{4 !}{3 !(4-3) !} \\& =4 ! / 3 ! \\& =4\end{aligned}[/tex]

Therefore, using combinations, we know that 4 different types of items will be selected.

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Answer:

Prime Numbers: 3,13,23,33

Composite Number: 9

Step-by-step explanation:

If a number has only 2 factors 1 and itself, then the number is prime

It is false that when two variables are highly correlated, a change in the value of one will cause a change in the value of another.

What is the variable of an equation?

An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 = 10. "X" in this case is a variable.

The fact that two variables are correlated does not mean that one causes the other.

False

If there is a causal relationship between two variables, then variables are correlated but it is not always true that if variables are correlated then there is a causal relationship.

Hence, it is false that when two variables are highly correlated, a change in the value of one will cause a change in the value of another.

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The statement best describing is only statistics for the ten states are reported

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. Statistics can be used to make future predictions calculate the likelihood that a given event will occur, or provide information about a survey. It primarily serves to convey knowledge, compute probabilities, and store records. In essence, it improves our understanding of the world by using numbers and other quantitative data.

In the given case, a total of ten states were selected by Judy and then the statical analysis was made. As per the given options, the correct option is that only statistics for the ten states are reported. This is because the number of terms, which are the states is ten.

Complete Question

Judy selected ten states and then calculated statistics on them. Which statement best describes the resulting statistics?

Only statistics for the ten states are reported.

No statistics are reported.

Statistics for all fifty U.S. states are reported.

The number of states included in the report depends on whether an attribute, interactive or spatial query was used to make the selection.

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A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

What do you mean by sampling?

Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.

According to the question,

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha =\frac{1-0.96}{2} =0.02[/tex]

Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex].

So it is z with a p value of [tex]1-0.02=0.98[/tex], so z= 2.055

Now, find the margin M as such

M = z*σ/√n

In which σ is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

σ = 40, M = 10,

M = z*σ/√n

[tex]10=2.055*\frac{40}{\sqrt{n} } \\10\sqrt{n}=82.2\\ \sqrt{n}=8.22\\ n=67.6[/tex]

Therefore, a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

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The probability that the mean of their test scores is greater than 78 is 0.0301.

Given,

Mean = 73

Standard Deviation σ = 7.8

Number of students randomly selected = 24

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

The number of standard deviations from the mean is called the z - score and can be found by the formula

Z = (x - μ)/σ.

Z = (70 - 73)/(7.8/√24) = -1.88442228

P(z < -1.88) = 0.0301

Therefore, P(z < -1.88) = 0.0301

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There may be missing data in a well-designed study because some respondents didn’t know the answer to the question, some respondents refused to answer the question and data for some respondents were lost or misrecorded. A random sample may no longer be random if you eliminate some members of the sample so eliminating might respondents with missing data compromise the results of a study

The first question is:

Missing data which of the following are valid reasons for why there may be missing data in a well-designed study? check all that apply.

The option 1, 2 and 3 may be possible reasons.

It is possible that some respondants did not know the answer of the question. Because it is not neccesary that every respondants know the answer of the quesions that are asked. So they can provide the wrong data and also not give the answer.

Some may refuse to answer because they don't want to answer or may be it is deficult to answer of those questions.

It may also possible that the the record were lost or misrecorded. Because there is lot of data that they have to organize and also possible there have many same detalis in the respondants that leads to the misrecoding.

The second question is:

Why might eliminating respondents with missing data compromise the results of a study?

If we eliminate a random sample then it is possible that the data may be biased and didn't involve the all factors. So it leads to wrong result and may harm the all process. So it directly effect the result of a study.

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