Which of the symbols correctly relates the two numbers below? Check all that
apply.
A. =
B. >
C. Z
☐ D. <
E. >
OF. s
364? 225

Answer:

3

Step-by-step explanation:

BT ≅ TD

[tex]19=5x+4\\15=5x\\3=x[/tex]

Answer:

[tex]\boxed{\mathrm\bold {4\dfrac{43}{72}}}[/tex]

Step-by-step explanation:

Let the unknown fraction be x

We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9

First convert 5 3/8 to an improper fraction for easier calculation

[tex]5 \dfrac{3}{8} = \dfrac{5\times 8 + 3}{8} = \dfrac{43}{8}[/tex]

Therefore we get:
[tex]\dfrac{7}{9} + x = 5\dfrac{3}{8}\\\\\dfrac{7}{9} + x = \dfrac{43}{8}\\\\[/tex]

Subtract  [tex]\dfrac{7}{9}[/tex]  on both sides to isolate x:

[tex]\dfrac{7}{9} - \dfrac{7}{9} + x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

[tex]x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

To compute the right side

a) The standard deviation of  1.45 mpg.

b)The margin of error for the mean estimate 3.03 mpg

c) A 95% confidence interval for μμ is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg, the mean highway mpg for this vehicle is  27 mpg.

a) Using the formula for the standard error of the mean, σx¯ = σ/√n, where σ is the standard deviation of the population, n is the sample size, we can calculate σx¯ = 6.5/√20 ≈ 1.45 mpg.

b) Using a 95% confidence level, we can find the critical value for the t-distribution with 19 degrees of freedom (n-1), which is 2.093. The margin of error for the mean estimate is then t*σx¯ = 2.093 x 1.45 ≈ 3.03 mpg.

c) The 95% confidence interval for μ is given by x¯ ± margin of error, which is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg. Since the vehicle sticker information states a highway average of 27 mpg, the results of this experiment are not consistent with the vehicle sticker, as the 95% confidence interval does not contain the value of 27 mpg. This suggests that the vehicle may not be performing as well as expected, or that the sample of mpg readings was not representative of the overall population.

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Answer:

[tex]x=-2(y+3)^2-4:[/tex]

Vertex: (-4, -3)

Focus: (-33/8, -3)

[tex]x=2(y-3)^2+4:[/tex]

Vertex: (4, 3)

Directrix: (x=31/8)

Step-by-step explanation:

Due to the formula being squared, you know it's going to be a parabola. The 4 at the end is to shift the parabola (-4 = left 4, 4 = right 4). From there you can deduce the vertex and from there the focus and directrix.

Answer:

  b = 30

Step-by-step explanation:

You want the value of b given line y = 20x +b passes through the points (6, 150) and (11, 250).

The equation y = 20x +b can be solved for b:

  b = y -20x . . . . . . . . subtract 20x

Using the given point (x, y) = (6, 150), you have ...

  b = 150 -20(6) = 150 -120

  b = 30

The sector angle are 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

We have to show the given data in a pie chart where each sector represents a proportion of a type of transportation.

39 students uses bus for transportation.

12 students uses bike for transportation.

25 students walk for transportation.

24 students uses car for transportation.

Total number of students = 39 + 12 + 25 + 24 = 100

Total sector angle of a circle = 360°

Sector angle for bus = (39 / 100) × 360 = 140.4°

Sector angle for bike = (12 / 100) × 360 = 43.2°

Sector angle for walk = (25 / 100) × 360 = 90°

Sector angle for car = (24 / 100) × 360 = 86.4°

Hence the sector angle for each mode of transportation is 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

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The answers include the following:

This is referred to as a mathematical operation in which two or more numbers or quantities are added together to form a sum.

3x = 18

x = 18/3 = 6

x+9 =22

x = 22-9 = 13

x/4 = 6

x = 6 × 4 = 24

x-12 =19

x = 19+12 =31

2x + 9 = 25

2x = 25-9 =16

x=16/2 = 8

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Answer:

5.15%

Step-by-step explanation:

Difference between estimated throw and actual throw

= estimated - actual

= 22.52 - 21.36

= 1.16 m

As a fraction of estimated throw:
1.16/22.52

As a percentage:
1.16/22.52  x 100 =  5.15%

The simplified expression is cos(x) of trigonometric expression  (sin (30° + x)+sin (30° - x))

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can simplify this expression using the sum-to-product formula for sine:

sin(a + b) + sin(a - b) = 2 sin(a) cos(b)

Let's use this formula by setting a = 30° and b = x:

sin(30° + x) + sin(30° - x) = 2 sin(30°) cos(x)

We know that sin(30°) = 1/2, so we can substitute:

sin(30° + x) + sin(30° - x) = 2(1/2) cos(x)

sin(30° + x) + sin(30° - x) = cos(x)

Therefore, the simplified expression is cos(x).

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Therefore, the area of the triangle ABC is approximately 18096.3 square units.

What is the area of the triangle?

To calculate the area of a triangle, use the formula area = 1/2 * base * height.

We can use Heron's formula to find the area of the triangle ABC when the lengths of its three sides are known:

[tex]Area = {\sqrt{(s(s-a)(s-b)(s-c))}[/tex]

where "s" is the semiperimeter of the triangle, which is half the sum of the lengths of its three sides:

s = (a + b + c)/2

In this case, we have:

a = AB = 154

b = BC = 346

c = AC = 349

So the semiperimeter is:

s = (a + b + c)/2 = (154 + 346 + 349)/2 = 424.5

Now we can use Heron's formula to find the area of the triangle

[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}\\\\Area = \sqrt{(424.5(424.5-154)(424.5-346)(424.5-349))}\\\\Area= 18096.3[/tex]

Therefore, the area of the triangle ABC is approximately 18096.3 square units.

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The linear functions for this problem are classified as follows:

a. Parallel.

b. Neither parallel nor perpendicular.

c. Perpendicular.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

They are classified as parallel, perpendicular or neither according to their slopes as follows:

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The following that are possible units for measuring mass in the metric system include the following below:

B. Kilogram

D. Gram.

This is a quantitative measure of inertia and it is referred to as the amount of matter which is present in a given body.

Options B and D both have the suffix "gram" which represents a metric system and are used in measuring mass unlike anagram which isn't a form of measurement which was why they were chosen as the correct set of options.

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For product=6 and sum=7, the numbers or integers  are 1 and 6.

What exactly are integers?

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

now,

As given product=6 and sum=7  

make factors for 6 i.e 1,2,3,6

from these choose the numbers whose sum=7

and they are 1,6.

Hence,

           For product=6 and sum=7, the numbers are 1 and 6.

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No, since interval contains 0, thus the difference between boys and girls is not significant.

This can be solved using the concept of standard deviation.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered.

We have given,

n₁ = 200,    n₂ = 150

x₁ = 48.4     x₂ = 48.9

s₁ = 12.96    s₂ = 11.85

95% confidence interval for difference of mean scores of boys and girls

since, n₁ and n₂ are very large therefore we may use standard normal variate , thus 95% CI is given by:

x₁ - x₂ ± 2μ₂ √(s₁²/n₁ + s₂²/n₂)

now, 2μ₂ = 1.96

∴ CI = (48.4 - 48.9) ± 1.96 √(12.96)²/ 200 + (11.85)²/150

or, CI = (-3.119, 2.1119)

no, since interval contains 0, thus the difference between boys and girls is not significant.

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Answer:

350

Step-by-step explanation:

∑ (xy) means the sum of the products of x and y , that is

∑ (xy)

= (7 × 2) + (2 × 5) + (5 × 7) + (9 × 4) + (6 × 2) + (10 × 9) + (9 × 9) + (8 × 4) + (4 × 10)

= 14 + 10 + 35 + 36 + 12 + 90 + 81 + 32 + 40

= 350

A) The homeownership rate in the United States calculated by the U.S. Census Bureau for the second quarter of 2019 as 64.1 percent means that about 64% of the U.S. homes are owner-occupied instead of renting.

B) The homeownership rate is the quotient of the number of owner-occupied homes and the total number of U.S. homes.

The homeownership rate describes the percentage or proportion of U.S. homes occupied by owners instead of renters.

The rate refers to the ratio, which is the relative size of one quantity compared to another.

To compute the homeownership rate, the number of owner-occupied homes is divided by the total number of U.S. homes and multiplied by 100.

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Answer:e

Step-by-step explanation:t

Answer:do homework

Step-by-step explanation:

The interest to be paid is $99

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Simple Interest = P×R×T/100

where P is the principal,

R is the rate

and T is the time

P = $900

R = 11%

T= 1

I = 900× 11/100

I = $99

therefore the interest to be paid is $99

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Answer: The simple interest on 16000 at 5% per annum for 1.5 years is calculated as:

I = P * r * t

I = 16000 * 0.05 * 1.5

I = 1200

The compound interest on 16000 at 5% per annum compounded half yearly for 1.5 years is calculated as:

A = P * (1 + r/n)^(nt)

A = 16000 * (1 + 0.05/2)^(2 * 1.5)

A = 16000 * (1.0253)^3

A = 16000 * 1.07897

A = 17253.576

The difference between the compound interest and simple interest is:

17253.576 - 1200 = 16053.576

So the difference between the simple interest and compound interest is 16053.576.

Step-by-step explanation:

Answer:

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

Definition:

Substitute for cos α:

A. Obtuse Triangle

B. Acute Triangle

C. Right Triangle

D. Right Triangle

What is meant by an obtuse triangle?

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or greater than 90°. Only 180° is equal to the internal angles of an acute triangle.

Given triangles are A. 15,16,17. B 20,18,7. C 17,144,145. D 24,32,40.

If the sum of squares of least two sides is greater than the square of the largest side then it is an obtuse triangle.

If the sum of squares of least two sides is less than the square of the largest side then it is an acute triangle.

If the sum of squares of least two sides is equal to the square of the largest side then it is a right triangle.

A. side lengths are 15,16,17

[tex]15^{2}+16^{2} =481\\17^{2} =289\\481 > 289[/tex]

Therefore this triangle is an obtuse triangle.

B. side lengths are 7,18,20

[tex]7^{2} +18^{2} =373\\20^{2}=400 \\373 < 400[/tex]

Therefore this triangle is an acute triangle.

C. side lengths are  17,144,145

[tex]17^{2} +144^{2} =21025\\145^{2}=21025 \\21025=21025[/tex]

Therefore this triangle is a right triangle.

D. side lengths are  24,32,40

[tex]24^{2} +32^{2} =1600\\40^{2}=1600 \\1600=1600[/tex]

Therefore this triangle is a right triangle.

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Answer:69

Step-by-step explanation:

31+38=69

The "value of x" in algebraic expression represented as "3x + 2 = 8" , in decimal form is 2.0   .

We have to solve the algebraic  expression "3x + 2 = 8" for value of x, we first need to separate the "variable x" on one side of the equation.

So , we subtract "2" from both sides of expression  ,

we get ;

⇒ 3x + 2 - 2 = 8 - 2  ;

Simplifying the left hand side, we get:

⇒ 3x = 6 ;

To solve for the variable x, we on divide both sides by 3 ;

⇒ 3x/3 = 6/3  ;

Simplifying, we get:

⇒ x = 6/3 = 2 .

Therefore, the value of x in the algebraic expression "3x + 2 = 8" is 2 , which is 2.0 when expressed as a decimal.

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The given question is incomplete , the complete question is

What is the value of x in the algebraic expression "3x + 2 = 8" ? Enter your answer, as a decimal . Do not round your answer.

On solving the provided question, we can say that equation is 532/13.5 = 39.4 doses.

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2.

the equation is the week * 7 (weekdays) * 24 (hours/day) * 19/6 (MILIGRAMS/HOURS)

532 mg per week (532/13.5 = 39.4 doses)

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Answer:

He will need 64 ft of fencing

Step-by-step explanation:

To determine the amount of fencing, we need to find the perimeter.

P = 2 (l+w)  where l is the length and w is the width

P = 2(22+10)

P = 2(32)

P = 64

He will need 64 ft of fencing

There will be about 95 counselors there with the help of expression 2375/50.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

Given that Total campers = 2375

and for each cabin there are 2 counselors and 50 campers

then no. of cabins = 2375/50

No. of counselors= 2*no. of cabins

=2*2375/50

=95

Hence,

            There will be about 95 counselors there with the help of expression 2375/50.

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Answer:

503.1222

rounded: 503.12

Step-by-step explanation:

The total distance biked by Yasmin on the first four days can be calculated as follows:

45 + 60 + 68 + 52 = 225 km

To find out how many kilometers she needs to bike on the last day to achieve an average of 58 km per day over the 5 days, we can set up an equation based on the formula for the mean:

(45 + 60 + 68 + 52 + x) / 5 = 58

Where x is the number of kilometers Yasmin needs to bike on the last day. Expanding the equation:

225 + x = 5 * 58

225 + x = 290

Subtracting 225 from both sides:

x = 65

So Yasmin needs to bike 65 kilometers on the last day to achieve an average of 58 kilometers per day over the 5 days

Answer:

  see attached

Step-by-step explanation:

You want the difference between horizontal shrink and vertical stretch.

A horizontal shrink compresses a graph horizontally. In the attached figure, the original graph is the red circle. The blue ellipse is that circle shrunk horizontally by a factor of 3. It retains the same height, but is compressed sideways.

A vertical stretch expands the graph vertically. The green ellipse in the attached figure is the original circle stretched vertically by a factor of 3. The horizontal dimension remains unchanged.

You will notice that replacing a variable x by x/k effectively accomplishes a stretch by a factor of k in that variable's direction. Similarly, replacing a variable x by kx accomplishes a compression by a factor of k.

Your question suggests that you have noticed the similarities between vertical stretch and horizontal compression. For some figures, there is basically no difference.

Here are a couple of examples of that:

  line y = x. Vertical stretch by 2: y/2 = x, or y = 2x. Horizontal compression by 2: y = 2x. These equations are identical.

  parabola y = x². Vertical stretch by 4: y/4 = x² or y = 4x². Horizontal compression by 2: y = (2x)² = 4x². These equations are identical.

The differences between stretch in one direction and compression in the other direction are more apparent for figures with multiple reversals of direction. The second attachment shows the sine function (red) vertically stretched (blue) and horizontally compressed (green).