The formula for finding the surface area of a rectangular solid with length 1, width w, ~ and height h is SA = 2/w + 21h + 2wh. Find the surface area of a rectangular solid with length 5 inches, width 2 inches, and height 4 inches. A. 28 square inches B. 36 square inches C. 72 square inches D. 76 square inches​

250 is the total surface area of the solid.

How do you determine surface area?

The whole surface of a three-dimensional form is referred to as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face.

                         Instead, you may write out the cuboid's length, width, and height and apply the formula surface area (SA)=2lw+2lh+2hw.

Each side of a cube with side length = 5  has an area of 25; the overall area is 6 x 25 = 150

A cube with sides of length 5 has an area of 25 on each side, making its overall area 6 x 25 or 150.

Both have a combined area of 150 + 150 = 300

300 - 25 - 25 = 250 is the result from each of the two cubes.

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Answer:

Step-by-step explanation:

Not sure.

Hypothesis testing is an important step when using sample data to estimate a population-level relationship because it helps ensure that the conclusions drawn from the data are accurate.

Hypothesis testing allows us to determine the probability that the observed results are due to chance, rather than reflecting a real relationship between the variables. When constructing a hypothesis, we set up two competing hypotheses, the null and the alternative. The null hypothesis states that there is no relationship between the variables and that the observed results are due to chance. The alternative hypothesis states that there is a relationship between the variables and that the observed results are not due to chance.

We can then use the sample data to conduct a test of statistical significance to compare the results of the two hypotheses. This test helps us determine whether the observed results are due to chance or if they are significant enough to suggest a real relationship between the variables. In conclusion, hypothesis testing is essential when using sample data to estimate a population-level relationship because it allows us to determine the probability that the observed results are due to chance, rather than reflecting a real relationship between the variables.

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A minimum score of 88.95 is required to receive an "A" grade on the exam.

To determine the minimum score required to receive an "A" grade on an exam, we must first understand the meaning of standard deviation and mean. The mean is the average of a set of values, whereas the standard deviation is a measure of how far apart the values are from the mean. The minimum score required to receive an "A" grade is determined by calculating the z-score that corresponds to the top 12.3 percent of exam scores.

The formula for calculating the z-score is given as: z = (x - μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. Solving for z, we have: z = invNorm(1 - 0.123) = invNorm(0.877) ≈ 1.15. The inverse normal distribution function is used to determine the value of z that corresponds to the area to the right of the z-score. We can then use the formula for the z-score to solve for the raw score (x):
x = zσ + μ
Substituting the values we have, we get:
x = 1.15(17) + 68 ≈ 88.95
Therefore, a minimum score of 88.95 is required to receive an "A" grade in the exam.

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Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.

We know that the cost per mile is $0.20, so we can set up an equation:

Cost = $20 + $0.20 x Distance

We can substitute $50 for Cost and solve for Distance:

$50 = $20 + $0.20 x Distance

$30 = $0.20 x Distance

Distance = $30 / $0.20

Distance = 150 miles

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The given statement regarding the GDP of major economies of the world is False.

To determine the accuracy of this statement, we would need to gather data on the real GDP per capita growth rates of major economies between 1982 and 2009 and compare them. Without this data, we cannot definitively say whether the statement is true or false. However, based on historical trends and current economic data, it is unlikely that Italy had the highest growth rate of real GDP per capita during this time period.

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Answer:

[tex]y-3=-\frac{3}{2}(x-2)[/tex]

Step-by-step explanation:

In order to find an equation that is parallel, it must have the same slope. This means the y intercept could literally be anything.

By equation of the line, we can write it in point slope form

[tex]y-y1=m(x-x1)[/tex]

where y1 and x1 are points on the coordinate plane and m is the slope.

We are already given the slope, so we just plug in the numbers.

[tex]y-3=-\frac{3}{2}(x-2)[/tex]

a) The sum of the given series is 7 / (1 + 2z)

b) The domain of convergence is (-∞, -1/2) U (1/2, ∞).

The given series can be expressed as

7 – 14z + 28z^2 - 56z^3 + ...

This is a geometric series with first term (a) = 7 and common ratio (r) = -2z. The formula for the sum of an infinite geometric series is

sum = a / (1 - r)

Substituting the values of a and r, we get

sum = 7 / (1 + 2z)

So, the sum of the given series is 7 / (1 + 2z).

For the series to converge, the absolute value of the common ratio must be less than 1. That is,

|r| = |−2z| < 1

Simplifying this inequality, we get

1/2 < |z|

So, the domain of convergence of the given series is (-∞, -1/2) U (1/2, ∞).

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The number of different ways to order 11 different pictures in a photo album is 39,916,800.

To calculate this number, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of items to choose from (in this case, 11 pictures) and r is the number of items to be selected (also 11, since we want to order all the pictures).

Plugging in the values, we get:

11! / (11 - 11)! = 11! / 0! = 11!

We can simplify 11! as:

11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Using a calculator or by hand, we can find that 11! equals 39,916,800.

Therefore, there are 39,916,800 different ways to order 11 different pictures in a photo album.

Hence, the number of ways to order 11 pictures in a photo album can be calculated using the permutation formula, which gives a total of 39,916,800 possible arrangements.

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The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2

A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:

ax^2 + bx + c = 0

If a quadratic function has only one root at 3, then it must be of the form:

f(x) = a(x - 3)^2

where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.

To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:

4 = a(0 - 3)^2

4 = 9a

a = 4/9

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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]

A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.

A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:

[tex]ax^2+bx+c=0[/tex]

If the quadratic function has only one root at 3, it must have the following form:

[tex]f(x)=a(x-3)^2[/tex]

This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.

We know that f(0) = 4, so we can plug these numbers into the equation to get:

[tex]4=a(0-3)^2[/tex]

simplify the above equation

4 = 9a

The value is,

a = 4/9

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Answer:

z = 32°

vertical angles are equal to each other. 32° ≅ z°

As a result, we should not be concerned that the sample does not accurately reflect the population.

We can learn more about average, population, and sample.

What is the population?

The entire group of people, items, or objects that we want to draw a conclusion about is known as the population. For example, if we want to learn about the average age of people in the United States, then the entire population is every individual in the United States.

What is a sample?

A smaller group of individuals, objects, or items that are selected from the population is known as a sample. A random sample is a sample in which every individual in the population has an equal chance of being selected for the sample.

What is an average?

A statistic that summarizes the central tendency of a group of numbers is known as an average.

The mean is the most commonly used average in statistics. The mean is calculated by adding up all the numbers in a group and then dividing by the number of numbers in the group. If we want to learn about the average salary of all teachers in the United States, we'd have to sample every teacher. That's not a feasible option. Instead, we take a smaller sample, which should be representative of the population, and then use the information gathered from that sample to make predictions about the population as a whole.

If we assume that the five teachers in the example are a random sample of all teachers in the United States, then we can conclude that the average salary of all teachers in the United States is around $49,000. As a result, we should not be concerned that the sample does not accurately reflect the population.

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The angle of elevation of the sun is 38.24 degrees (rounded to two decimal places).

The ratio of the height of the tree and the length of the shadow can be found by using the formula for tan which is given by:

tan(x) = (opposite/hypotenuse)

In the given problem statement, the height of the tree is opposite to the angle we are trying to find and the length of the shadow is the hypotenuse of the right-angled triangle. Therefore, we can say that:

tan(x) = opposite/hypotenuse = 86/110

We can use the inverse tangent function to find the value of x. This is because tan is the ratio of the opposite side (height of the tree) to the adjacent side (length of the shadow), and the inverse tangent function gives the angle that has that ratio.

So, tan x = 86/110 => x = tan⁻¹ (86/110) = 38.24 degrees (rounded to two decimal places). Therefore, the angle of elevation of the sun is 38.24 degrees.

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Answer:

x = ±9

Step-by-step explanation:

If x² = k, then x = ±√k.

x² - 81 = 0

x² = 81

x = ±√81

x = ±9

The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.

Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:

P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]

P(X>=10) = 0.719

Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.

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Samantha would fill in the following information on the survey sheet based on the data provided:

Sex: Female

Age: 13-14

How much pressure do you feel to achieve at school? c. A lot

Samantha, a 14-year-old girl, would complete the survey slip by selecting "Female" under "Sex," "13-14" under "Age," and "A lot" under "How much pressure do you feel to achieve at school?"

This indicates that Samantha is feeling a significant amount of pressure to succeed academically. It's common for high school students to feel pressure to perform well in school, and this can be due to various factors such as parental expectations, college aspirations, or personal goals.

As a school counselor, it's essential to understand the level of pressure students are experiencing to provide appropriate support and guidance. Identifying and addressing the sources of pressure can help students like Samantha better manage stress and achieve academic success.

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The question is -

A school counselor conducted a survey among a group of high school students using the following survey slip:

Survey (please tick the correct boxes)

Sex:  Male  Female

Age:  13-14  15 -16  17–18

How much pressure do you feel to achieve at school?

a. None b. A little c. A lot  And d. the unbearable amount

Show, by completing the survey slip on the answer sheet, how Samantha – a 14-year-old girl who feels a lot of pressure to achieve at school – would complete the survey

Answer:

Let's call the length of the hypotenuse SD as x.

Since the altitude from T to SD divides SD into two parts, let the length of the shorter part be y. Then the length of the longer part is x-y.

Using similar triangles, we have:

TU/TS = ST/TD

Substituting the values we have:

TU/(3√5) = √5/UD

TU = (3/5)UD

Using the Pythagorean theorem in triangle TUS, we have:

TU² + (3√5)² = TS²

(3/5 UD)² + 45 = ST²

9/25 UD² + 45 = ST²

Using the Pythagorean theorem in triangle TUD, we have:

TU² + UD² = TD²

(3/5 UD)² + UD² = x²

9/25 UD² + UD² = x²

34/25 UD² = x²

UD² = (25/34)x²

Substituting the value of UD² in the equation ST² = 9/25 UD² + 45, we get:

ST² = 9/25 (25/34)x² + 45

ST² = 45/34 x² + 45

Since y = x-y-1, we have y = (x-1)/2.

Using the Pythagorean theorem in triangle TUD, we have:

(1/4) (x-1)² + UD² = x²

(1/4) (x² - 2x + 1) + (25/34)x² = x²

(1/4)(x²) + (25/34)x² - (1/2)x + (1/4) = 0

(59/68)x² - (1/2)x + (1/4) = 0

Using the quadratic formula, we get:

x = [1/2 ± √(1/4 - 4(59/68)(1/4))]/(2(59/68))

x = [1/2 ± (3√34)/17]/(59/34)

x = 17/59 ± 6√34/59

Since x is the hypotenuse SD, we have:

UD² = (25/34) x²

UD² = (25/34) [(17/59 ± 6√34/59)²]

UD² = 136/59 ± 204√34/295

Therefore, the exact lengths of the two parts of the hypotenuse are:

SD = x = 17/59 ± 6√34/59

SU = x-y = (x-1)/2 = 8/59 ± 3√34/59

UD = y = (x-1)/2 = 8/59 ± 3√34/59

TU = (3/5) UD = (3/5) [8/59 ± 3√34/59] = 24/295 ± 9√34/295

ST² = 45/34 x² + 45 = 45/34 [(17/59 ± 6√34/59)²] + 45

ST = √[45/34 [(17/59 ± 6√34/59)²] + 45]

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.

given

The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.

To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.

As a result, we have:

sin 30° = (6/2x)

Adding two times to both sides:

2x * sin 30° = 6

Using sin 30°, which has a value of 0.5:

x = (6/(2 * 0.5)) = 6/1 = 6

Consequently, the side YZ is 6 units long.

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

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The value of x given the following image is 13.

What is congruent angle?

When two angles have the same magnitude, they are considered congruent. In other words, they have the same angle degree. For example, if one angle measures 45 degrees, any other angle that also measures 45 degrees is congruent to it.

Congruent angles are denoted by the symbol ≅. So, if angle A and angle B have the same measure, we can write it as:

Angle A ≅ Angle B

Congruent angles have the same properties and characteristics, including being able to fit into the same spaces and be formed by the same geometric shapes. In practical terms, congruent angles are identical when placed side by side.

Finding the value of x :

Angle ABC and Angle EBD are congruent.

Value of Angle ABC is (-3x+14) degrees.

Value of Angle EBD is (-x-12) degrees.

Equating the two angles we get ,

[tex]-3x+14=-x-12[/tex]

[tex]-2x=-26[/tex]

[tex]2x=26[/tex]

[tex]x=13[/tex]

Therefore, the value of x given the following image is 13.

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The transformation that would not result in a congruent figure when performed on triangle RST is A. A dilation by a scale factor of 2 with respect to point R.

The equation that has the same solution as the system of equations is C. 4x + 9y = 10

4x + 6y = 24.

Transformations that change the shape or size of a figure can change its congruency.  A dilation is a transformation that changes the size of a figure so this would mean that RST dilated would not result in a congruent figure.

When the system of equations, 4x + 9y = 10, 2x + 3y = 12 is solved, we find that x = 13 and y = - 14/ 3.

Options A,B, and D cannot have the same value because the numbers are the same and so they should have different values., Only option C can be the same and when the values are slotted in, this is proven.

Option C, 4x + 9y = 10 , 4x + 6y = 24 is therefore correct.

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⇒First take out the highest common factor 2 form the quadratic equation and divide each and every term of that equation by that common factor.

⇒Factorise the equation and equate the factors of the equation to 0 and solve for the unknown variable x.

⇒Below are the steps on solving for the unknown variable.

[tex]2(x^{2} -14x+49)=0 \\\frac{2(x^{2} -14x+49)}{2} =\frac{0}{2} \\x^{2} -14x+49=0\\(x-7)(x-7)=0\\x-7=0\\x=7[/tex]

There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.

In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).

Therefore, the calculation is as follows:

total number of ways = nCr

                    = 5C4

                    = 5! / 4!(5-4)!

                    = 5! / 4!1!

                    = 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1

                    = 5 x 4 x 3 x 2

                    = 120

Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

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The fact that the sample averages are not all the same can be an illustration of the concept of the central limit theorem, while the fact that the sample averages systematically overestimate the true population average can be an illustration of the concept of bias.

The given statement is incomplete, we need additional information in order to provide a solution. It is important to provide the complete statement so that we can help you in the best way possible.

However, based on the given options, we can provide a general explanation of the concepts mentioned, which are the concepts of the central limit theorem and bias.

The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases. In other words, as the sample size increases, the means of the samples drawn from a population tend to be normally distributed. The central limit theorem has important implications for statistics and hypothesis testing.

Bias, on the other hand, refers to a systematic error in data collection or analysis. Bias can be caused by a variety of factors, such as the selection of participants or the measurement instruments used. A biased sample or analysis can lead to inaccurate conclusions about a population.

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To perform the opposite translation, we add the opposite of the translation vector to the image point A': the coordinates of point A are (16, 5).

what is a vector?

In mathematics, a vector is an object that represents a quantity having both magnitude (or length) and direction. Vectors can be represented geometrically as arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.

To find the coordinates of point A, we need to perform the opposite translation of moving along the vector 〈−6, 0〉 from the image point A'(10, 5). This is because a translation is a rigid motion that preserves the distance between points, so the distance between A and A' is the same as the distance between their respective translations.

To perform the opposite translation, we add the opposite of the translation vector to the image point A':

A = A' - 〈-6, 0〉 = (10, 5) - (-6, 0) = (16, 5)

Therefore, the coordinates of point A are (16, 5).

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The equations without absolute value for the given conditions are: 1. y = -3x + 6 if x > 5; 2. y = -x - 6 if x < -2; 3. y = x - 6 if 3 ≤ x ≤ 5, and y = -x - 6 if x < 3.

1. When x > 5, the expression (x - 3) is positive, (x + 2) is positive, and (x - 5) is positive. Thus, to get absolute value we can rewrite the equation as:

y = (x - 3) + (x + 2) - (x - 5)

Simplifying this, we get:

y = 2x - 4

2. When x < -2, the expression (x - 3) is negative, (x + 2) is negative, and (x - 5) is negative. Thus, we can rewrite the equation as:

y = -(x - 3) - (x + 2) + (x - 5)

Simplifying this, we get:

y = -2x + 6

3. When -2 ≤ x ≤ 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is negative. Thus, we can rewrite the equation as:

y = -(x - 3) + (x + 2) - (x - 5)

Simplifying this, we get:

y = 10 - x

When x > 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is positive. Thus, we can rewrite the equation as:

y = -(x - 3) + (x + 2) + (x - 5)

Simplifying this, we get:

y = -2x + 6

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Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 7 !

__________________

hope it helps ⸙

Answer:

Eighty biscuits.

Step-by-step explanation:

We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits

[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]

We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.

[tex]Biscuits=4*20=80[/tex]

Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.

[tex]Flour:\\1000-4(180) = 280g[/tex]

After making 4 servings we still have 280g of flour left.

The probability that a person chosen at random has run a red light in the last year can be calculated by taking the number of people who said “yes” to running a red light and dividing it by the total number of people in the group.

For example, if 10 people said “yes” and 20 said “no”, the probability of a person chosen at random running a red light in the last year is 10/30, or 1/3.

The probability of an event happening is calculated using the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcome is running a red light in the last year, and the total number of outcomes is the total number of people asked.

To calculate the probability, we take the number of people who said “yes” to running a red light in the last year and divide it by the total number of people in the group. In our example, 10/30 = 1/3, so the probability that a person chosen at random has run a red light in the last year is 1/3.

In conclusion, the probability of a person chosen at random having run a red light in the last year is calculated by taking the number of people who responded “yes” and dividing it by the total number of people in the group.

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