Geometry
Show work and if you’re a slow kid then don’t answer

The correct Option is A. Equation that can be used to find the number of dogs in the shelter is StartFraction 60 divided by 2 Over 100 divided by 2 EndFraction = StartFraction 30 Over 50 EndFraction.

In order to do that, we first need to determine the number of dogs in the shelter.

We can do that by multiplying the total number of animals by 60% (0.60):60% of 50 = (60/100) × 50 = 30

Therefore, there are 30 dogs in the shelter.

Now, we can look at the answer choices to see which equation can be used to find the number of dogs in the shelter.

A. (60/2 ÷ 100/2) = 30/50This equation simplifies to (30 ÷ 50) = 0.6, which is the decimal equivalent of 60%. T

his equation is correct.

B. (100 × 2 ÷ 50 × 2) = 200/100

This equation simplifies to 1, which is not the correct answer.

C. (50 ÷ 1 ÷ 60 ÷ 1) = 50/60

This equation simplifies to 5/6, which is not the correct answer.

D. (60 × 2 ÷ 50 × 2) = 120/100

This equation simplifies to 6/5, which is not the correct answer.

Therefore, the equation that can be used to find the number of dogs in the shelter is A. (60/2 ÷ 100/2) = 30/50.

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The amount that Miguel originally put into the bank is given as follows:

$728.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

Then the interest accrued is given as follows:

I(t) = Prt.

In which the parameters of the equation are listed and explained as follows:

The interest accrued from the first year to the second year is of $30.28, hence the rate is given as follows:

30.28 = 757.12r

r = 30.28/757.12

r = 0.04.

Then the principal is obtained as follows:

1.04P = 757.12

P = 757.12/1.04

P = $728.

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Drake is correct, and Selena is incorrect in this scenario.Option D.

Selena's Work:

Selena substituted the values for the variables r = -1 and s = -2 directly into the expression before simplifying. She then simplified the expression and evaluated it.

However, this approach is incorrect because the order of operations requires simplification before substitution. Selena should have simplified the expression first and then substituted the values of r and s.

Drake's Work:

Drake followed the correct order of operations. He simplified the expression first and then substituted the values of r = -1 and s = -2. By simplifying the expression, Drake obtained (-1/-2), which simplifies to 1/2. After substituting the values, Drake evaluated the expression correctly and arrived at the final result of 1/2.

Since Drake followed the correct order of operations and obtained the correct result, he is the one who is correct. Selena's mistake was in not simplifying the expression before substituting the values for r and s.

In mathematical operations, it is important to follow the order of operations (PEMDAS/BODMAS) to ensure accurate results. The correct order is to simplify the expression first, and then substitute the given values for the variables. So Option D is correct.

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The method that you find important to enhance the strong number sense is  the use of manipulatives and hands-on activities.

Example:

Illustrating numbers and executing mathematical operations through block representations can assist students in visualizing addition, subtraction, and multiplication.

Using manipulatives and interactive activities, numerical concepts can be grasped more tangibly, as learners physically engage with these objects, thereby developing a concrete understanding of mathematics.

Students can enhance their comprehension of measurement and units by employing measurement instruments such as rulers and measuring tapes.

Through participation in these tasks, students cultivate a profound sense of intuition in regard to numbers, operations, and their interconnections, thereby establishing a firm groundwork.

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The solution to this integral [tex]\int\limits^{\infty} _{-\infty} e^{-x^{2} } \, dx =\sqrt{\pi}[/tex] is equal to √π.

In Mathematics, the Gaussian integral is sometimes referred to as the probability integral, and it highly related to the erf function, which represents the integral of the one-dimensional Gaussian function over the interval [-∞, ∞].

Generally speaking, the given integral can be computed by using the advanced techniques of combining two one-dimensional Gaussians and converting into polar coordinates;

[tex]I^2 =\int\int e^{(-(x^2 +y^2))}dxdy\\\\I^2 =\int\int e^{-r^2}rdr d\theta[/tex]

In this context, we would use these integration limits [0, ∞) with respect to "r" and [0, 2π] with respect to "θ" as follows:

[tex]I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0} e^{-r^2}rdr d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0}\frac{1}{2} e^{-u}du d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} [\frac{1}{2} e^{-u}]\limits^{\infty}_{0}d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} (\frac{1}{2} )d\theta\\\\I^2=\frac{1}{2}[\theta]\limits^{2 \pi}_{0}\\\\I^2=\frac{1}{2}(2 \pi)-\frac{1}{2}(0)\\\\I^2=\frac{2 \pi}{2}[/tex]

I² = π

I = √π

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The polygons that can be regarded as similar polygons are A and D.

Similar polygons are those whose sizes may vary but whose shapes are the same. To put it another way, they have proportional sides and corresponding angles that are equivalent. The geometric likeness or resemblance between them is referred to as being "similar".

Similar polygons have corresponding angles with the same measurements. For instance, if a right angle exists in one polygon, another polygon with a comparable angle will likewise have a right angle. Similar to this, if an angle in one polygon is 60 degrees, the comparable angle in a related polygon will also be 60 degrees.

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Answer:

h=1.8 cm

Step-by-step explanation:

Solution Given:

Volume of triangular prism= Area of base * length

Here

Volume of traingular Prism= 63 cm³

base =7 cm

length =10 cm

Area of base = Area of triangle=½*base*height=½*7*h

Now

substituting value in the formula:

63= ½*7*h*10

63=35*h

h=63/35

h=1.8 cm

Therefore, height of the triangular cross section is 1.8 cm.

Considering the triangles, the value of BE is 27

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

In the figure, BE is solved using the following ratio

FD / FA = DC / AE

1 / 2 = 27 / AE

AE = 27 * 2

AE  = 54

BE = 1/2 AE

BE = 27

hence BE = 27

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Answer:

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

Solve the given equation in below steps:

Answer:

For both problems, the correct equation of the line will be presented in three forms.

14)

y - 4 = -5(x + 1)---point-slope form

y - 4 = -5x - 5

y = -5x + 1---slope-intercept form

5x + y = 1---standard form

15)

y + 3x = 13

y = -3x + 13

y - 10 = (1/3)(x - 6)---point-slope form

y - 10 = (1/3)x - 2

y = (1/3)x + 8---slope-intercept form

3y = x + 24

-x + 3y = 24---standard form

x - 3y = -24

Answer: A= -1, B= -3,C=-4.D=3 i think

Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.

Based on the given statements, we can make the following inference:

If the time is between 8:00 a.m. and 3:00 p.m., then the bank is open.

If the bank is open, then people may make withdrawals or deposits.

Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.

The inference follows the logical flow of the given statements.

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The calculated measure of x in the circle is 2

From the question, we have the following parameters that can be used in our computation:

The circle

The measure of x in the circle can be calculated using the angle intersected by arc theorem

So, we have

1/2(69x + 2) = 70

Multiply both sides by 2

69x + 2 = 140

So, we have

69x = 138

Divide both sides by 69

x = 2

Hence, the measure of x in the circle is 2

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The set of ordered pairs that represents a function is:

{(−1,6),(0,−3),(5,−9),(−1,3)}

In a function, each input value (x-coordinate) must be paired with only one output value (y-coordinate). In the given set, there are no repeated x-coordinates, meaning that each input value is associated with only one output value. Therefore, it satisfies the definition of a function.

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

To determine how the mean changes when a value of 120.5° is added to the data, we need to recalculate the mean before and after the addition.

Given the average high temperatures:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

To find the original mean, we sum up all the temperatures and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 904 / 12 = 75.33°

Now, let's add the value of 120.5° to the data:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 120.5

To find the new mean, we sum up all the temperatures (including the added value) and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 120.5) / 13 = 1025.5 / 13 ≈ 78.88°

The mean has increased from 75.33° to 78.88°.

Therefore, the mean increases by approximately 3.55° (rounded to the nearest tenth).

The correct answer is: The mean increases by 3.5°.

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

The value that is the input of the function is 4.

A function relates input and output. In other words,  a function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The independent variable is the x values or the input value while the dependent variable is the y values of the output values.

Hence, the values of the input(x) of the function are 4, 6, 8, 10. 12 etc.

Therefore, base on the option, the input of the function is 4.

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The graph that represents the piecewise function, h(x) is the second option

Please find attached the graph that represents h(x) created with MS Excel

A piecewise function comprises of two or more functions, which are defined based on specified intervals of the input variable.

The possible piecewise function that is represented by h(x), obtained from a similar question on the site can be presented as follows;

[tex]h(x) \begin{cases} \frac{1}{4}\cdot x-4, & \text{ } x\leq0 \\\frac{1}{3}\cdot x - 3, & \text{ } 0 < x \leq 3 \\\frac{1}{2}\cdot x-2, & \text{ } x\geq4\end{cases}[/tex]

Therefore, at x ≤ 0, the y-intercept is -4, for h(x) = (1/4)·x - 4, which corresponds to the second graph.

The range for h(x) at 0 < x ≤ 3 is; h(0) = (1/3)×0 - 3 < h(x) ≤ (1/3)×3 - 3, which can be expressed as; (-3, -2], also corresponding to the second graph

The value of x-intercept of h(x) in the interval x ≥ 4 can be found from the equation; h(x) = (1/2)·x - 2 = 0

(1/2)·x = 2

x = 2 × 2 = 4

The x-intercept, (4, 0), corresponds to the second graph, therefore, the graph that represents h(x) is the second graph

Please find attached the graph that represents the piecewise function, h(x), created with MS Excel

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a. Domain -   [0, 20]

b. Range -   [8, ∞)

c. X-intercepts -   undefined.

d. Y-intercept -   8

e. Missing function value f(9) = 11

a. The function's domain is the range of x-values over which the graph is defined.  In this case, the domain is from 0 to 20, inclusive -   [0, 20].

b. The function's range is the set of all possible y-values that the function takes. Since the graph starts from unit 8 on the y-axis, the range would be from 8 to positive infinity -   [8, ∞).

c. since the   graph does not touch the x- axis at any point, we can state that the there is no x-intercept orthat the x -intercept is undefined.

d. The y-intercept is the point where the   graph intersects the y-axis. In this case, the y-intercept is at unit 8 on the y-axis.

e.  Based on the graph the point (9, 11) corresponds to the value of y when x is 9, then f(9) would be equal to 11.

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Answer:

A = -5

B = -2

C = 3

Step-by-step explanation:

[tex](A) = (-3)^{2} +4(-3)-2\\(A) = 9+(-12)-2\\(A) = -5\\\\\\(B) = (0)^{2} +4(0)-2\\(B)=0+0-2\\(B)=-2\\\\\\(C)=(1)^{2} +4(1)-2\\(C)=1+4-2\\(C)=3[/tex]

Answer:

The answer is approximately 11 stories

Step-by-step explanation:

6 stories------->22 meters

x stories---------->40 meters

[tex]x = \frac{6 \times 40}{22} [/tex]

x≈11 stories

The options that represent arithmetic sequences are A) 2n - 1, C) 3n + 4, and D) 5n - 2.

To determine which of the given general terms represents an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Let's evaluate each option:

A) 2n - 1

To find the difference between consecutive terms, we subtract the general term for the (n+1)th position from the general term for the nth position:

[(2(n+1)) - 1] - (2n - 1) = 2n + 2 - 1 - 2n + 1 = 2

Since the difference between consecutive terms is 2, option A) 2n - 1 represents an arithmetic sequence with a common difference of 2.

B) n^2 + 3

Let's calculate the difference between consecutive terms:

[(n+1)^2 + 3] - (n^2 + 3) = n^2 + 2n + 1 + 3 - n^2 - 3 = 2n + 1

The difference between consecutive terms is 2n + 1, which is not a constant value. Therefore, option B) n^2 + 3 does not represent an arithmetic sequence.

C) 3n + 4

Calculating the difference between consecutive terms:

[(3(n+1)) + 4] - (3n + 4) = 3n + 3 + 4 - 3n - 4 = 3

The difference between consecutive terms is 3, which is a constant value. Therefore, option C) 3n + 4 represents an arithmetic sequence with a common difference of 3.

D) 5n - 2

Finding the difference between consecutive terms:

[(5(n+1)) - 2] - (5n - 2) = 5n + 5 - 2 - 5n + 2 = 3

The difference between consecutive terms is 3, which is a constant value. Therefore, option D) 5n - 2 represents an arithmetic sequence with a common difference of 3.

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Question

which one of the following general term of sequence is arithmetic?​

A) 2n - 1

B) n^2 + 3

C) 3n + 4

D) 5n - 2

The value of is 2/11

To determine the value, we have;

Index forms are mathematical forms used to represent numbers or values that are too large or too small in more convenient forms.

From the information given, we have the expression written as;

2⁹ˣ+2 = 16⁵ˣ -2

Put all the terms in one base form, we have;

2⁹ˣ + 2¹ = 2²⁰ˣ - 2¹

equate the exponents, we have;

9x + 1 = 20x - 1

collect the like terms, we have;

9x - 20x = -2

-11x = -2

Make 'x' the subject of formula, we have;

x = 2/11

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Answer: First row: 6,12,15

              Second row: 15

Step-by-step explanation:

For first row: 3*1, 3*2, 3*3, 3*4, 3*5

Second row: 5*1, 5*2, 5*3, 5*4, 5*5

The equality of angle A and angle C is proved by Side-Angle-Side theorem (SAS).

The proof of similarity of the triangles is determined by applying angle - angle (AA) theorem as shown below.

angle A will be equal to angle C if the following condition is met;

triangle BAG ≅ triangle DCG

From the given diagram, by reflexive similarity;

line BG = line DG

line BA = line DC

line GA = line GC

Since all the side lengths are congruent to each other and ΔBGA is equal to ΔDGC, then angle A must be equal to angle C.

Thus, the equality of angle A and angle C is proved by Side-Angle-Side theorem.

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The correct answer is Option B. 50 chairs can John make in 5 hours from the graph.

John is a furniture maker and the graph shows the number of chairs John makes and the time it takes to make those chairs.

Based on the graph, the number of chairs John can make in 5 hours can be found by following the given steps:

Step 1: Look for the point on the graph where the line intersects the vertical line marking 5 hours.

Step 2: From the point on the graph found in step 1, read the horizontal line and find the point at which it intersects the y-axis.

This point will give us the number of chairs John can make in 5 hours.

According to the graph, John makes 50 chairs in 5 hours.

Therefore, the correct answer is option (B) 50.

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The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

Answer:

ok, here is your answer

Step-by-step explanation:

If the sales tax is 3%, then the tax amount Lucy will pay on the silver coat rack priced at $69 would be:

Tax amount = 3% of $69

Tax amount = (3/100) * $69

Tax amount = $2.07

Therefore, Lucy will pay $2.07 in tax.

Answer:

The final purchase price is 71.07

Step-by-step explanation:

First step is to determine the amount of tax:

69*3%

69 * .03

2.07

Now add the tax to the purchase price:

69+2.07

71.07

The final purchase price is 71.07

We can conclude that ∠AOM ≅ ∠MOD.

Given that AC, MN, and DB intersect at point O, we can prove that ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON. This can be shown using the vertical angles theorem.

By the given information, we know that ∠BON ≅ ∠NOC. Using the transitive property of congruence, we can conclude that ∠AOM ≅ ∠MOD.

In other words, since AC, MN, and DB intersect at point O, we have the following angle relationships: ∠BON ≅ ∠NOC and ∠AOM ≅ ∠MOD.

The given information states that ∠BON ≅ ∠NOC. Using the vertical angles theorem, we can infer that ∠AOM ≅ ∠NOC. Furthermore, since ∠AOM ≅ ∠NOC and ∠BON ≅ ∠NOC, we can apply the transitive property of congruence to conclude that ∠AOM ≅ ∠MOD.

Therefore, we have successfully proved that ∠AOM ≅ ∠MOD based on the given intersecting line segments and angle relationships.

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Answer:

c = 50

Step-by-step explanation:

2c - 3 = 97

2c = 100

c = 50

Answer:

V = 1/3 π r^2 h

Step-by-step explanation:

V = 1/3 area base*height

1. work out the area

2. base*height

3. area*answer

4. you get full answer