The grades of a science test are normally distributed. Thanh finds that his grade on the test has a z-score of â€""2. 5. Which statement must be true? Thanh’s grade is 2. 5 standard deviations below the mean of the test grades. Thanh’s grade is 2. 5 points below the mean of the test grades. Thanh’s grade is 2. 5 standard deviations above the mean of the test grades. Thanh’s grade is 2. 5 points above the mean of the test grades.

Answer: The volume of a sphere of radius 3cm is 113.143cm3. Note- In order to solve this question, we must know the formula of the volume of the sphere i.e. 43πr3.

The formula for the volume of a sphere is V = 4/3 π r³, where V = volume and r = radius.

For example: Because your formula tells you to cube the radius. Since the radius is in inches, then you also cube your inches. Thus your answer is 267.95 inches cubed. Now, if your radius was 4 feet instead of 4 inches, then your answer would be 267.95 feet cubed.

Final Answer = 113.143cm3.

Step-by-step explanation:

The graph of the quadratic function x²+4x=-2x+16 is a parabola that crosses the x-axis at x=-8 and x=2. Correct option is (a).

Let ax² +bx +c = 0 is an quadratic equation its zeroes are the values of x for which the Left hand side becomes zero.

To find zeroes we can use quadratic formula that is

x = (-b ±√(b²-4ac))/2

Graph of the quadratic equation are points ( x , y(x) )

where y(x) =  ax² +bx +c

when x= t is zero of quadratic equation ax² +bx +c = 0

then y(t) = 0

(t, 0) points are points on the x-axis.

Given an quadratic equation

x²+4x=-2x+16 has roots x =-8 and x =2

This can we written as  x² +6x -16 =0

The graph of  this quadratic equation is given by (x, y(x))

where y = x² +6x -16 which is a parabola

for x= -8 and x= 2 , y(-8) =y(2) = 0

Then (-8,0)  and (2,0) are points on this parabola which are at x-axis

Therefore, the parabola y = x² +6x -16  crosses the x-axis at x=-8 and x=2.Thus (a) is the correct option.

Also learn more about the quadratic equations from the link below:

https://brainly.com/question/1863222

#SPJ2

On average, the number of miles the athlete ran per day is; 18/5 or 3.6 miles per day

We are given;

Number of days the athletes ran = 3¹/₂ days = 7/2 days

Total distance ran in the given time = 12³/₅ miles = 63/5 miles

Now, the average distance will simply be given by the expression;

Average Distance = Total Distance/Number of days of running

Now, let us convert the fractions to improper fraction for easy division. Thus, we have;

Number of days the athletes ran = 7/2 days

Total distance ran in the given time = 63/5 miles

Thus;

Average Distance = (63/5)/(7/2)

Average distance = 63/5 * 2/7 = 18/5 = 3.6 miles per day

Read more about Average distance at; https://brainly.com/question/4931057

#SPJ1

The function P is given by:

Substitute t=0 into the formula:

Therefore, the number of insects at t=0 is 200

Answer: 32.5

Step-by-step explanation: you divide it.

Using the concept of ratio and proportion, the vendor sold 56 cups of hot cider.

The word "proportion" often denotes a portion, share, or sum that is in comparison to a whole. Two ratios are in proportion when they are equal, according to the proportional idea. When an equation or a statement to that effect is used, two ratios or fractions are equal.

A percentage is a mathematical comparison of two numbers. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.

Cider supplied by the street seller for value = x for 35

= x/35

The cider's ratio is 8:5,

x/35 :: 8:5,

x = [35(8)]/ 5

=56.

To know more about ratio, visit:

https://brainly.com/question/13419413

#SPJ4

Using the probability concept, the proportion of times do we expect the practitioner to guess the correct hand is of 0.44.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

The probability can be interpreted as the proportion of times that we expect a trial to happen.

In the context of this problem, this probability is of 44%, as stated for Emily's model, that is, out of 100 trials, the correct answer was obtained in 44 of them, hence the proportion of times do we expect the practitioner to guess the correct hand is of 0.44.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

Step-by-step explanation:

Sample Space

off  even numbers

= {2,4,6,8,10}.

There are 5 outcomes in the sample space,

Answer:

y = -4x + 16

Step-by-step explanation:

The slope of the given line is -4

when two lines are parallel, their slopes are equal

That means the slope of the second line is -4 too

Thus, we have to use the point-slope form to write the equation

That will be

y-y1 = m(x-x1)

y-8 = -4(x-2)

y -8 = -4x + 8

y = -4x + 8+8

y = -4x + 16

According to the quantity equation, the answer is option (a) $2,250.

the value of M when Y = 3,000, P = 3, and V = 4. The quantity equation is represented as MV = PY. To solve for M, follow these steps:

1. Substitute the given values into the equation: M * 4 = 3 * 3,000
2. Simplify the equation: 4M = 9,000
3. Divide both sides by 4: M = 9,000 / 4
4. Calculate the value of M: M = 2,250

So, when Y = 3,000, P = 3, and V = 4, the value of M is $2,250 (option a).

Learn more about quantity equation

brainly.com/question/28837405

#SPJ11

Answer:

25

Step-by-step explanation:

v^2 - 10v + __ : what number when added to itself gives you -10 ? -5

what's -5 x -5 ? 25

(v-5)^2 is a perfect square

Answer:

15.3 dollars

Step-by-step explanation:

13.50 + (.09 x 20 = 1.8)

13.50 + 1.8

The blue line represents the curve of the function that is being integrated. The green line represents the area under the curve between the lower and upper limits of integration. The yellow line represents the area between the two points on the curve. The red dot is the lower limit of integration, and the yellow dot is the upper limit of integration.

Integration is a way of finding the area under a function. The lower limit of integration is the point at which the area starts to be measured, while the upper limit of integration is the point at which the area stops being measured.

When calculating the area under the curve between two points, the lower and upper limits of integration can be identified by the red and yellow dots.

To calculate the area between the two points, we will use the formula for integration. This involves taking the integral of the function between the lower and upper limits of integration. This is done by summing the area of each small slice of the function between the two points.

Once the area under the curve is found, it can be compared to the area represented by the green line. If the green line is larger than the area under the curve, then the area under the curve will be negative. If the area under the curve is larger than the green line, then the area under the curve will be positive.

By comparing the green line to the area under the curve, it is possible to determine whether the area is positive or negative. This can help to solve mathematical problems that require integration.

Know more about integration here:

https://brainly.com/question/988162

#SPJ11

Answer:

Step-by-step explanation:

solve for X+3<_4  and  X+3<_-4

Step-by-step explanation:

solve for x+3/<4

please mark me as brilliant and gives a thank

2 is the y-coordinate for the solution.

To find the y-coordinate for the solution to the system of equations, we will substitute the value of y into the first equation.

Given the system of equations:

x + 3y = 9 (Equation 1)

y = 2x/3 (Equation 2)

Since Equation 2 gives us y in terms of x, we can substitute this expression into Equation 1:

x + 3(2x/3) = 9

Simplifying the equation, we have:

x + 2x = 9

3x = 9

x = 3

Now, we can substitute the value of x back into Equation 2 to find the corresponding y-coordinate:

y = 2(3)/3

y = 2

Therefore, the solution to the system of equations is x = 3 and y = 2.

The y-coordinate for the solution is 2.

Know more about coordinate here:

https://brainly.com/question/30227780

#SPJ11

Part A

Let's say we measure a board length and we measure 18.639 cm. Now let's say we round to the nearest tenth. That would lead to 18.6 cm. The question is "What is the largest value we can measure such that we round to the nearest tenth to get 18.7 cm?"

Well we could measure 18.7 cm exactly, but there are values we could measure that are larger to round to that value. We could measure 18.71 or 18.72, etc etc all the way up to 18.74; once we get to 18.75, it will round to 18.8

So this means that the largest we can measure is 18.74 and it is the upper bound we're after.

=========================================================

Part B

We use the same idea as part A, but now we're extending out one more decimal place.

We could measure 58.37 cm exactly or we could measure 58.371 or we could do 58.372, etc until we arrive at 58.374

By the time we get to 58.375, it will round to 58.38 and that's not what we're after. So the highest we can go is 58.374 cm

The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

For more questions on Value.

https://brainly.com/question/843074

#SPJ8

In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

to know more about value refer here

brainly.com/question/30145972#

#SPJ11

Answer: personaly i would choose C

Step-by-step explanation:

the -25 is bigger than the 2 so it will be a negative answer

The following are the variables that could be of interest to generate environmental data: Pollution levels: Pollution levels are a measure of the degree to which the air is contaminated.

Contaminants in the air, such as particulate matter and toxic gases, can be hazardous to human health and the environment, and monitoring them can provide valuable data on air quality.Air quality: Air quality refers to the level of pollution in the air. This could include measurements of various pollutants, such as nitrogen dioxide, sulfur dioxide, and particulate matter. This data can be gathered by a variety of sensors, including gas analyzers, particle counters, and spectrometers.Ozone concentration: Ozone concentration refers to the amount of ozone in the air. Ozone is a powerful oxidant that can have both beneficial and harmful effects on human health and the environment. Storm intensity: Storm intensity refers to the severity of a storm.

This could include measurements of wind speed, rainfall, and lightning activity. Data on storm intensity can be gathered using weather stations, Doppler radar, and lightning detection systems.Vegetation density: Vegetation density is a measure of how much plant life is present in a given area. This data can be used to monitor changes in ecosystems over time and to assess the impact of human activities on the environment. Vegetation density can be measured using satellite imagery, ground-based surveys, and remote sensing technologies.Earthquake intensity: Earthquake intensity refers to the strength of an earthquake. This could include measurements of ground motion, ground acceleration, and ground displacement. Data on earthquake intensity can be gathered using seismometers and other ground-based sensors. Wildlife diversity can be measured using a variety of techniques, including surveys, camera traps, and acoustic monitoring.

To know more about interest visit:

https://brainly.com/question/30393144

#SPJ11

On evaluating the given expression we get -9.6. We use the BEDMAS rule where we solve Brackets, Exponents, Division, Multiplication, Addition and Subtraction in a given expression in this order.

We evaluate the the problem using BEDMAS rule:

2.(|3.4-6|-1.8)÷2 1/2+(-2)^3

= 2.(|12-6|-8) ÷ 5/2 + (-8)

= 2.(6-8) ÷ 5/2 - 8

=2.(-2) ÷ 5/2 - 8

= -4 ÷ 5/2 - 8

= -8/5 - 8

= -48/5

= -9.6

Thus the answer of the the given expression we get after evaluating it is -9.6

Another problem on evaluating the expression using BEDMAS

brainly.com/question/24105090

#SPJ4

Answer:

The slope is -5

Step-by-step explanation:

For every 1 value moved in the x value, the line goes 5 values down. This means the slope is -5/1 or -5.

I hope that this helps! :)

Answer:

  a) discrete

  b) D: {1, 2, 3}; R: {3, 4}

  c) is a function

Step-by-step explanation:

When the graph is made up of individual dots, it represents a discrete function.

__

The domain is the set of x-coordinates of the points on the graph:

  domain: (1, 2, 3}

The range is the set of y-coordinates of the points on the graph:

  range: {3, 4}

__

No vertical line intersects the graph in more than one place, so the graph is a function.

Answer:

The conclusion is false.

Step-by-step explanation:

If the conclusion is false, then the whole conditional is false even if the hypothesis is true.

There will be 30 trucks when there are 5 cars, maintaining the 1:6 ratio.

Given that the ratio of cars to trucks is 1:6, we can determine the number of trucks by multiplying the number of cars by the ratio. If there are 5 cars, we can calculate the number of trucks using the ratio.

Let's assume the number of trucks as "x." According to the given ratio, we have the equation:

1 car : 6 trucks = 5 cars : x trucks

To solve for x, we can set up a proportion:

1/6 = 5/x

Cross-multiplying, we get:

1 * x = 6 * 5

x = 30

Therefore, there will be 30 trucks when there are 5 cars, based on the given ratio of 1:6.

Alternatively, we can calculate the number of trucks by dividing the number of cars by the fraction representing the ratio:

Number of trucks = (Number of cars) / (Ratio of cars to trucks)

Number of trucks = 5 / (1/6)

Number of trucks = 5 * (6/1)

Number of trucks = 30

So, there will be 30 trucks when there are 5 cars, maintaining the 1:6 ratio.

For more such questions on ratio, click on:

https://brainly.com/question/12024093

#SPJ8

Answer:

The other one is 1 and the top number 6

Step-by-step explanation:

Heres why: the rest are indiosncrys and ploasery

Answer:

1.75² ------> Expanded form: 1.75 x 1.75 ------> Standard Form: 1.75²

= 3.0625

1/4³ ------> Expanded form: 1/4 x 1/4 x 1/4 or .25 x .25 x .25 ------> Standard Form: 1/4³ =0.015625

Step-by-step explanation:

Please tell me if I am wrong.  

Hope this helps.

:]

a) The 90% confidence interval for the population mean is approximately (21.52, 23.48).

b) The 95% confidence interval for the population mean is approximately (21.322, 23.678).

c) The 99% confidence interval for the population mean is approximately (20.926, 24.074).

To develop confidence intervals for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

where the standard error is equal to the sample standard deviation divided by the square root of the sample size.

a) For a 90% confidence interval, we need to find the critical value corresponding to a confidence level of 90%. The critical value can be obtained from the t-distribution table with (n-1) degrees of freedom. Since the sample size is 56, the degrees of freedom is 56-1 = 55.

From the t-distribution table, the critical value for a 90% confidence interval with 55 degrees of freedom is approximately 1.671.

The standard error can be calculated as:

Standard Error = sample standard deviation / sqrt(sample size)

Standard Error = 4.4 / sqrt(56)

Standard Error ≈ 0.5882

Now we can calculate the confidence interval:

Confidence Interval = 22.5 ± (1.671 * 0.5882)

Confidence Interval = 22.5 ± 0.9816

Confidence Interval ≈ (21.52, 23.48)

b) For a 95% confidence interval, the critical value for 55 degrees of freedom is approximately 2.004 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.004 * 0.5882)

Confidence Interval = 22.5 ± 1.178

Confidence Interval ≈ (21.322, 23.678)

c) For a 99% confidence interval, the critical value for 55 degrees of freedom is approximately 2.678 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.678 * 0.5882)

Confidence Interval = 22.5 ± 1.574

Confidence Interval ≈ (20.926, 24.074)

For more such question on mean visit:

https://brainly.com/question/1136789

#SPJ8

Answer:

The lines are certainly not parallel!

Step-by-step explanation:

The slope of line J is 3/2, while the slope of line k is exactly 1 :)

Answer:ITS C!!!! :))

Step-by-step explanation: