state the modal numbers
1,2,3,4,5,6,7

Answer:

[tex]2\sqrt{65}[/tex] cm, decimal form is about 16.1 cm

Step-by-step explanation:

Use the pythagorean theorem:

A^2 + B^2 = C^2

A and B are legs, c is hypotenuse

First leg is 16, second leg is 2

Plug it in:

16^2 + 2^2 = hypotenuse^2

256 + 4 = hypotenuse ^2

260 = h^2

[tex]\sqrt[2]{260}[/tex] = h

To simplify the square root of 260, we can factor 260 into its prime factors:

260 = 2 x 2 x 5 x 13

Then, we can take out the pairs of identical factors from under the square root symbol:

sqrt(260) = sqrt(2 x 2 x 5 x 13)

= sqrt(2 x 2) x sqrt(5) x sqrt(13)

= 2sqrt(65)

[tex]2\sqrt{65}[/tex]

Answer:

16.2 or 16.00

Step-by-step explanation:

Leg #1 --->16

Leg #2 --->2

C ---> hypotenuse

16.12452---->16.12

16.12 rounded to the nearest tenth is 16.00

The key features of the given quadratic equation include the following:

Vertex = (-2, 4)

Axis of symmetry: x = -2.

Direction of opening: downward.

There is a maximum (max) at 4.

y-intercept = (0, 0).

roots: x = -4 and x = 0.

In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the graph of this quadratic equation, we can reasonably infer and logically deduce that its vertex can be determined as follows:

y = -2(x + 2)² +4

Vertex, (h, k) = (-2, 4)

Axis of symmetry, Xmax = -2.

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At sunrise, shadows are longest and point towards the west as the sun rises in the east. Therefore, the correct order would be:

Longest shadows of the day, and they point to the west → shadows gradually become shorter → very short shadows or no shadows → shadows gradually become longer → longest shadows of the day, and they point to the east.

As the sun moves across the sky, shadows change in length and direction, reaching their shortest length at noon when the sun is directly overhead. After noon, the sun starts to move towards the west, and shadows gradually become longer until sunset when they are longest again, but this time pointing towards the east as the sun sets in the west.

Therefore, correct order of descriptions of shadows during the day, from sunrise to sunset, would be:

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See text below



How do shadows change during the day?

Drag and drop the descriptions of shadows to show the correct order, from sunrise to sunset.

longest shadows of the day, and they point to the west

longest shadows of the day, and they point to the east

shadows gradually become shorter

very short shadows or no shadows

shadows gradually become longer

Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.

Toshi's prediction was that he would perform the card trick successfully 95% of the time. This means that out of 100 card tricks, he expects to perform the trick successfully in 95 of them. We can represent this mathematically by:

P(success) = 0.95

This is the probability of success for one card trick.

Toshi actually performed the card trick 30 times and was successful in 24 of them. We can represent this as:

P(actual success) = 24/30 = 0.8

This is the proportion of successful card tricks that Toshi actually performed.

To compare Toshi's prediction with his actual results, we can use probability theory. The probability of getting exactly x successes in n trials when the probability of success is p is given by the binomial distribution formula:

P(x) = (n choose x) * pˣ * [tex](1-p)^(n-x)[/tex]

In this case, we can use the formula to calculate the probability of getting exactly 24 successes in 30 trials if Toshi's prediction of 95% success rate is accurate. This is given by:

P(24 successes) = (30 choose 24) * 0.95²⁴ * 0.05⁶ ≈ 0.0045

This means that if Toshi's prediction is accurate, the probability of getting exactly 24 successes in 30 trials is very low (less than 0.5%).

Therefore, we can conclude that Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

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The value of x is 3 unit.

The correct option is B.

We have,

P = 3√2/2

Angle= 45

Using Trigonometry

cos 45 = B /H

1/√2 = ( 3√2/2)/ x

x= 3√2/2 . √2

x = 6/2

x= 3 unit

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The Surface area of the triangular prism is 26.88 cm².

The Volume of the triangular prism is 7.68 cm³.

The formulas we would used are:

Surface area of triangular prism = (S1 + S2 + S3)(L) + bh

Volume of triangular prism = 1/2 * base * height * length of prism

Perimeter of the triangular face = (S1 + S2 + S3) = 4.0 + 3.2 + 2.4 = 9.6 cm

Length of prism = 2.0 cm

base of triangular face (b) = 3.2 cm

height of triangular face (h) = 2.4 cm

Plug in the values:

Surface area of triangular prism = (9.6)(2.0) + (3.2)(2.4) = 26.88 cm²

Volume of triangular prism = 1/2 * 3.2 * 2.4 * 2.0 = 7.68 cm³

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In the number 425.871, the digit with the greatest value is 4 because it is in the hundreds place, representing a value of 400.

In the number 425.871, each digit has a position and a value based on where it's located in the number. The position starting from the right of the decimal point we call the tenths, hundredths, and thousandths place, respectively. Similarly, the position to the left of the decimal point is called the ones, tens, hundreds place, etc., respectively. In this case, the digit with the greatest value is the one in the hundreds place, which is 4. This is because it represents 400, which is greater than any other individual digit's value in the number 425.871.

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A z-score is a statistical measurement that indicates how many standard deviations an individual value is from the mean - True.

The mean from the value of interest and dividing the result by the standard deviation.

This standardized score provides a way to compare values from different data sets or populations.

For example, if a student's score on a test is 80 and the mean score for the class is 70 with a standard deviation of 5, the student's z-score would be 2.

This means that the student's score is two standard deviations above the class mean. This information can be useful in understanding the student's performance relative to their peers.

Z-scores can also be used to identify outliers or extreme values in a data set. Values with a z-score greater than 3 or less than -3 are considered to be outliers and may warrant further investigation.

In summary, a z-score is a valuable tool in statistical analysis that measures how many standard deviations a value is from the mean. It provides a standardized way to compare values across different data sets and can help identify outliers or extreme values.

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Answer:

5

Step-by-step explanation:

Answer:

15 grams

Step-by-step explanation:

Based on the information provided, the weight of each hummingbird is 2.5 grams, 3 grams, 4.5 grams, and 5 grams. To find the total weight of all 4 hummingbirds combined, we can add up their individual weights: 2.5 + 3 + 4.5 + 5 = 15 grams. So, the total weight of all 4 hummingbirds combined is 15 grams.

The solution to the system by elimination is (-2, 4).

To solve the system using elimination, we need to eliminate one of the variables by multiplying one or both of the equations by a constant.

-6X = 18 - Y

9 = -3X - 8Y

Rewrite as

-6X = 18 - Y

3X = 9 - 8Y

So, we have

-6X = 18 - Y

6X = 18 - 8Y

Now we can add this equations to the second equation to eliminate x:

0 = 36 - 9Y

This gives

9Y = 36

So, we have

Y = 4

Recall that

-6X = 18 - Y

So, we have

-6X = 18 - 4

So, we have

-6X = 12

Divide by 2

X = -2

Therefore, the solution to the system is (-2, 4).

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The correct option is- A. graph of two lines with the intersecting point at (negative 1, 1).

On a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Given system of equations:

y + 2x = −1  ...eq 1

3y − x = 4 ..eq 2

multiply eq 2 with 2 and add to eq 1

6y − 2x = 8 ..eq 3

6y − 2x + y + 2x = 8 - 1

7y = -7

x = -1

Now,

y + 2x = −1

y + 2(-1) = −1

y = -1 + 2

y = 1

Thus, the solution of the given system of equations. y + 2x = −1 and 3y − x = 4 is found as :(-1, 1).

The graph for the equations are attached.

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Correct question:

Choose the correct graph of the given system of equations. y + 2x = −1 and 3y − x = 4 .

Group of answer choices :

A. graph of two lines that intersect at the point (negative 1, 1)

B. graph of two lines that intersect at the point (1, 1) < Not

C. graph of two parallel lines with positive slopes

D. None of the above

Answer:

(3,0)

Step-by-step explanation:

the point (5,-5) a translation of 2 units left would be equivalent to x-2.

(5-2,-5)

5 units up is equivalent to y+5

therefore

(5-2,-5+5)

yields

(3,0)

Answer: Looks pretty good :) !

The experimental probability that you will roll a three on your next roll is 70%.

To calculate the experimental probability of rolling a number three on the next roll, we need to use the data given in the problem. Out of the 20 rolls that were performed, the number three was rolled 14 times.

The experimental probability is calculated by dividing the number of times the event occurred (in this case, rolling a number three) by the total number of trials.

So, the experimental probability of rolling a number three on the next roll is:

14/20 or 7/10

This means that based on the data from the previous 20 rolls, there is a 70% chance of rolling a number three on the next roll.

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The equation that represents the line of best fit is given as follows:

y = 50x.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

When x = 10, y = 500, hence the slope m is given as follows:

m = 500/10

m = 50.

Hence the equation is given as follows:

y = 50x.

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Answer:

[tex]r = \sqrt{ {3}^{2} + {( - 7)}^{2} } = \sqrt{9 + 49} = \sqrt{58} [/tex]

[tex] {x}^{2} + {y}^{2} = 58[/tex]

the vegetable garden is 24 square feet larger than the herb garden. The area of the square vegetable garden is equal to the length of one side squared.

what is  larger than  ?

"larger than" is a comparative term used to describe a situation where one thing has a greater size, quantity, value, or magnitude than another thing. It is used to indicate a comparison between two or more objects or quantities.

In the given question,

The area of the square vegetable garden is equal to the length of one side squared. Each side of the square garden is 6 feet long, so the area of the vegetable garden is:

6 feet × 6 feet = 36 square feet

The area of the rectangular herb garden is equal to its length multiplied by its width. The length of the herb garden is 4 feet and the width is 3 feet, so the area of the herb garden is:

4 feet × 3 feet = 12 square feet

To find the difference in area between the two gardens, we subtract the area of the herb garden from the area of the vegetable garden:

36 square feet - 12 square feet = 24 square feet

Therefore, the vegetable garden is 24 square feet larger than the herb garden.

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Therefore, the solution to the equation 10ˣ = 23 is: x = log(23) that is option B.

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be solved to find the value(s) of the variable(s) that make the equation true.

Here,

Taking the logarithm of both sides of the equation 10ˣ = 23:

log(10ˣ) = log(23)

Using the power rule of logarithms, the left-hand side simplifies to:

x log(10) = x

Since log(10) = 1, we have:

x = log(23)

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Answer:

160°/360° = area/(π(5^2))

area = 25π(4/9) = 100π/9 square inches

Circumference = (4/9)π(5) = 20π/9 inches

The projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).

Explain the term projection

Projection is the process of representing a three-dimensional object or scene onto a two-dimensional surface. It involves the use of mathematical principles to create a flat image that accurately depicts the shape and position of the object or scene. Projections are widely used in fields such as engineering, architecture, and computer graphics to create visual representations of complex structures and designs.

According to the given information

The projection of a vector u onto a vector v is given by the formula proj_v(u) = (u•v)/(||v||²) * v, where u•v is the dot product of u and v, and ||v|| is the magnitude of v.

In this case, u = (-9,-5) and v = (-6,5). The dot product of u and v is u•v = (-9)(-6) + (-5)(5) = 54 - 25 = 29. The magnitude of v is ||v|| = √((-6)² + (5)²) =

√(36 + 25) = √61.

So the projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).

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The test statistic (3.46) is greater than the critical value (2.05), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.02 level to support the company's claim that above 61% of the chips do not fail in the first 1000 hours of their use.

The null hypothesis for this scenario is that the proportion of computer chips that do not fail in the first 1000 hours of their use is equal to or less than 61%, while the alternative hypothesis is that the proportion is greater than 61%. Mathematically:

H0: p ≤ 0.61

Ha: p > 0.61

where p is the true proportion of computer chips that do not fail in the first 1000 hours of their use.

To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:

z = (0.64 - 0.61) / sqrt((0.61 * 0.39) / 1600) = 3.46

where 0.39 is the complement of 0.61, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.02 level of significance is 2.05.

Since the test statistic (3.46) is greater than the critical value (2.05), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.02 level to support the company's claim that above 61% of the chips do not fail in the first 1000 hours of their use.

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The Hardy-Weinberg equation is a mathematical formula used to calculate the frequency of alleles (alternative forms of genes) in a population.

It states that the frequency of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.

The equation is expressed as: p² + 2pq + q² = 1

In this equation, p represents the frequency of the dominant allele in the population, and q represents the frequency of the recessive allele.

The superscripts 2 represent the proportion of individuals in the population that are homozygous for that allele (meaning they have two copies of the same allele), while the 2pq term represents the proportion of individuals that are heterozygous (meaning they have one copy of each allele).

The sum of these terms is always equal to 1, as it represents the entire population.

This equation assumes several conditions: that the population is large, randomly mating, with no mutations, migration, natural selection, or genetic drift.

In reality, these conditions are rarely met, and the Hardy-Weinberg equation serves as a useful model for understanding how allele frequencies can change over time due to various evolutionary influences.

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A. The area of the rectangle is 29.16 square inches.

B. The width of the rectangle is 2.7 inches and the height (or length) is 10.8 inches

A parallelogram in which each pair of adjacent sides is perpendicular is referred to as a rectangle.

We should utilize "w" to address the width and "l" to address the length of the square shape.

A. Since the width equals one quarter of the length, we are able to write:

w = (1/4)l

We also know that the perimeter of the rectangle is 27 inches, and

the formula for the perimeter of a rectangle is:

P = 2l + 2w

Substituting the first equation into the second equation, we get:

P = 2l + 2(1/4)l

27 = 2.5l

l = 10.8

Now that we know the length, we can use the first equation to find the width:

w = (1/4)l

w = (1/4)(10.8)

w = 2.7

As a result, the rectangle has a width of 2.7 inches and a height of 10.8 inches.

B. To find the area of the rectangle, we can use the formula:

Area = length *width

Substituting the values we found above, we get:

A = (2.7)*(10.8)

A = 29.16

Therefore, the area of the rectangle is 29.16 square inches.

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Answer:

7) 760

8) 34

Step-by-step explanation:

7)  95x8=760

8)  (103-35)/2=34

The correct statement about the numbers is,

⇒ The number is even or less than 12.

We have to given that;

A number is selected at random from the set (2, 3, 4.... 10).

Hence, We can check all the options as;

⇒ 10 is divisible by 5

Hence, A is incorrect.

⇒ Since, 2 = 2

Hence, B is incorrect.

⇒ Since, Every numbers are less than 12 and some numbers are even.

Hence, The correct statement about the numbers is,

⇒ The number is even or less than 12.

Thus, The correct statement about the numbers is,

⇒ The number is even or less than 12.

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Answer: Symbol max-min and answer 10-4

Step-by-step explanation:

Answer:

Starting at the origin (0, 0), go right 3 units, then down 7 units. You will end at (3, -7).