The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 50%, interpret the likelihood of randomly selecting a terrier from the shelter.

Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event

Answer:

Ther answers are in the photo I've added

Step-by-step explanation:

Use trigonometry:

4.

[tex] \tan(60°) = \frac{bc}{15} [/tex]

Cross-multiply to find the value of BC:

[tex]bc = 15 \times \tan(60°) = 15 \sqrt{3} [/tex]

∠B = 180° - 60° - 90° = 30° (the sum of all triangle's angles is 180°)

To find AB, we can use the Pythagorean theorem:

[tex] {ab}^{2} = {ac}^{2} + {bc}^{2} [/tex]

[tex] {ab}^{2} = {15}^{2} + ({15 \sqrt{3} )}^{2} = 225 + 675 = 900[/tex]

[tex]ab > 0[/tex]

[tex]ab = \sqrt{900} = 30[/tex]

Now we the others one the same way

.

5.

[tex] \tan(45°) = \frac{40}{qs} [/tex]

[tex]qs = \frac{40}{ \tan(45°) } = 40[/tex]

∠R = 180° - 90° - 45° = 45°

[tex] {rs}^{2} = {qr}^{2} + {qs}^{2} [/tex]

[tex] {rs}^{2} = {40}^{2} + {40}^{2} = 3200[/tex]

[tex]rs > 0[/tex]

[tex]rs = \sqrt{3200} = 40 \sqrt{2} [/tex]

.

6.

[tex] \sin(53°) = \frac{dc}{21} [/tex]

[tex]dc = 21 \times \sin(53°) ≈16.77[/tex]

∠D = 180° - 90° - 53° = 37°

[tex] {bc}^{2} = {bd}^{2} - {dc}^{2} [/tex]

[tex] {bc}^{2} = {21}^{2} - ({16.77})^{2} = 159.7671[/tex]

[tex]bc > 0[/tex]

[tex]bc = \sqrt{159.7671} ≈12.64[/tex]

the coefficient of the squared term in the equation of this parabola is -1/9.

what is parabola ?

A parabola is a type of symmetrical curve that is defined by a set of points in a plane. It is a conic section, meaning it is formed by the intersection of a plane and a cone. A parabola has a U-shape and can be either upward-facing or downward-facing, depending on its equation.

In the given question,

If the vertex of a parabola is at (h,k), then the equation of the parabola can be written in vertex form as y = a(x - h)² + k, where "a" is the coefficient of the squared term.

We are given that the vertex of the parabola is at (1,-4), so we can write:

y = a(x - 1)² - 4

We are also given that when the y-value is -5, the x-value is 4. Substituting these values into the equation, we get:

-5 = a(4 - 1)² - 4

Simplifying this equation, we get:

-5 = 9a - 4

9a = -1

a = -1/9

Therefore, the coefficient of the squared term in the equation of this parabola is -1/9.

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Answer:

The highest card already drawn is the 10 of hearts, so we need to find the probability that the next card drawn is a jack, queen, king, or ace. There are 16 of these cards in the deck (4 jacks, 4 queens, 4 kings, and 4 aces) out of a total of 47 cards left in the deck (since 5 cards have already been drawn).

Therefore, the probability of drawing a winning card is 16/47, which is approximately 0.34 or 34%. None of the given answer choices match this calculation, so there must be a mistake in the problem or in the answer choices.

The required, probability of drawing a winning card is 25%. Option D is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

There are 52 - 4 = 48 cards remaining in the deck after the 4 cards have been drawn. To win, the player needs to draw a card with a value higher than 10. There are 3 aces and 3 jacks, 3 queens, and 3 kings left in the deck that can satisfy this condition, for a total of 12 winning cards.

Therefore, the probability of drawing a winning card is:

P(winning) = number of winning cards/number of remaining cards

= 12 / 48

= 1 / 4

= 25%

So, the answer is D. 25%.

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Answer:y = 9x - 1

Step-by-step explanation:

Calculate the slope (m) using the two points (x1, y1) = (2, 17) and (x2, y2) = (-7, -64):

m = (y2 - y1) / (x2 - x1)

m = (-64 - 17) / (-7 - 2)

m = (-81) / (-9)

m = 9

Now that we have the slope (m = 9), we can use one of the points (either (2, 17) or (-7, -64)) to find the y-intercept (b). Let's use (2, 17):

y = mx + b

17 = 9 * 2 + b

17 = 18 + b

b = -1

Now we have the slope (m = 9) and the y-intercept (b = -1), so we can write the equation of the line in the form y = mx + b:

y = 9x - 1

Since the point (-4, a) is on the graph of y = x², the value of a is equal to 16.

In Mathematics and Geometry, a quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Where:

When x = -4, the value of y or a can be calculated as follows;

y = x²

y = a = (-4)²

y = a = 16.

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check the image for the explanation

Answer:

degree of -2x^4 is 4

degree of -3 is 0

degree of 4x^6 is 6

degree of -6x^7 is 7

degree of the polynomial 17

Step-by-step explanation:

the degree of a term is the exponent of the variable. so for the terms, just write down the exponent of X. since -3 does not have a variable, it has a degree of 0. the degree of a polynomial is the sum of the exponents on all variables so 4+6+7=17.

If the given integer is positive, then it is plotted to the right of zero on the number line. If the given integer negative, then it is plotted to the left of zero on the number line.

For the augmented matrix,

1. Row 1 multiplied by -5 is

[tex]\left[\begin{array}{cccc}20&-30&25&15\\-2&4&0&-3\\2&-6&1&-1\end{array}\right][/tex]

2. Row 1 interchanged with row 3

[tex]\left[\begin{array}{cccc}2&-6&1&-1\\-2&4&0&-3\\20&-30&25&15\end{array}\right][/tex]

3. Row 1 multiplied by -2 and added to row 3

[tex]\left[\begin{array}{cccc}2&-6&1&-1\\-2&4&0&-3\\16&42&23&17\end{array}\right][/tex]

An augmented matrix can be described as a rectangular shaped array of numbers that represents a system of linear equations. These numbers are arranged in rows and colums. They can differ  in sizes depending on the array of numbers in the matrix.

The above answer is in response to the questions below as seen in the picture.

Perform the indicated row operation on the given augmented matrix.

[-4 6 -5 -3, -2 4 0 -3, 2 -6  1  -1]

a. Multiply row 1 by -5

[_ _ _ _, _ _ _ _, _ _ _ _]

b. interchange row 1 and row 3

[_ _ _ _, _ _ _ _, _ _ _ _]

c. Multiply row 1 by -2 and add to row 3

[_ _ _ _, _ _ _ _, _ _ _ _]

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(1) The closest answer choice is B. 0.148 repeated, which is equivalent to 0.148148... (2) The closest answer choice to the value of the shaded area is A. 0.148.

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.

(1) If the shaded area is 2/12 of the total area, we can simplify 2/12 by dividing both the numerator and denominator by 2, which gives us 1/6. So, the shaded area is 1/6 of the total area.

Let's assume that the total area of the diagram is 1 unit, then the shaded area would be:

1/6 x 1 = 0.166666...

This value is equal to 0.166666... or 0.1666 with 4 decimal places, which is not exactly equal to any of the answer choices provided.

The closest answer choice is B. 0.148 repeated, which is equivalent to 0.148148... with the digits repeating infinitely. However, this is not exactly equal to the calculated value of 0.166666....

Therefore, none of the answer choices provided is an exact match for the calculated value of the shaded area.

(2) If the shaded area is 2/15 of the total area, then we can find the value of the shaded area as follows:

Let's assume that the total area of the diagram is 1 unit, then the shaded area would be:

2/15 x 1 = 0.133333...

This value is equivalent to 0.1333 with 4 decimal places, which is not exactly equal to any of the answer choices provided.

The closest answer choice is A. 0.148, which is approximately equal to the calculated value of 0.133333... but is not an exact match.

Therefore, the closest answer choice to the value of the shaded area is A. 0.148.

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Answer:

b= 51°  c= 129°

Step-by-step explanation:

We know that angle b = 51° as it is a verticle angle to 51°. To find angle c, we must know that on a straight angle, there is a total of 180°.

180° = angle 1 + angle 2.

Since we know one of the angles, we can plug it into the equation,
180° = 51° + c

-51°         -51°

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

180° - 51° = c

129° = c

Answer:

FD = 16 units

Step-by-step explanation:

The possible solutions are (1,2), (1,5), (3,4). So correct options are B, C, and D.

In mathematics, an inequality is a statement that compares two values or expressions using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Inequalities are used to represent a range of values that satisfy a certain condition, rather than just a single value.

For example, the inequality x > 5 represents all the possible values of x that are greater than 5. This can include 6, 7, 8, and so on. Similarly, the inequality y ≤ 2x + 1 represents all the possible values of y that are less than or equal to 2 times x plus 1.

Inequalities can be graphed on a number line or in the coordinate plane to show the range of values that satisfy the inequality. They are commonly used in solving problems involving equations, functions, and systems of equations.

We can graph the two inequalities to find the solutions that satisfy both.

The graph of y > 4x - 3 is a blue dashed line with a slope of 4 and y-intercept of -3. We shade the region above the line since the inequality is "greater than".

The graph of y ≥ -2x + 3 is a green dashed line with a slope of -2 and y-intercept of 3. We shade the region above the line since the inequality includes "greater than or equal to".

The shaded regions overlap in the upper-right quadrant, so any point in that region satisfies both inequalities. Looking at the options given:

A. (1,1): Does not satisfy y > 4x - 3

B. (1,2): Satisfies both inequalities

C. (1,5): Satisfies both inequalities

D. (3,4): Satisfies both inequalities

E. (0,5): Satisfies y ≥ -2x + 3 but not y > 4x - 3

Therefore, the possible solutions are B, C, and D.

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(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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8 feet is the distance between the ground and the top of the ladder

Given the following sides

length of ladder = hyp = 10foot

Distance from ladder to the base = adjacent  = 6 feet

Substitute the given parameters into the formula to have:

10² = opp² + 6²

opp²=100 - 36

opp² = 64

Take square root on both sides

opp = 8 feet

Hence, 8 feet is the distance between the ground and the top of the ladder

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Answer:

Diego will need 21 gallons of yellow paint to make the shade of green paint he desires.

Step-by-step explanation:

According to the given information, Diego wants to make a shade of green paint that requires 3 parts yellow and 7 parts blue.

This means that for every 7 gallons of blue paint, Diego needs 3 gallons of yellow paint.

As Diego is using 49 gallons of blue paint, we can set up the following proportion:

7/49 = 3/x

where x is the amount of yellow paint needed.

To solve for x, we can cross-multiply and simplify:

7x = 3 * 49

7x = 147

x = 21

Therefore, Diego will need 21 gallons of yellow paint to make the shade of green paint he desires.

Taylor series will be

4 - 2x² + (2x⁴ / 3) - (2x⁶ / 45) + ...

The Taylor series for a function f(x) centered at a is given by:

f(x) = Σ [[tex]f^n[/tex](a) / n!] * [tex](x-a)^n[/tex](n from 0 to infinity)

where [tex]f^n[/tex])(a) denotes the nth derivative of f evaluated at x=a.

To find the first four nonzero terms of the Taylor series for f(x) = 4cos²(x) centered at a=0, we need to compute the derivatives of f(x) and evaluate them at x=0.

f(x) = 4cos²(x)

f'(x) = -8cos(x)sin(x) = -4sin(2x)

f''(x) = -8cos(2x)

f'''(x) = 16sin(2x)

f''''(x) = 32cos(2x)

Now we can plug these values into the formula for the Taylor series to obtain:

f(x) = f(0) + f'(0)x + (f''(0)x² / 2!) + (f'''(0)x³ / 3!) + (f''''(0)x⁴ / 4!) + ...

f(0) = 4cos²(0) = 4

f'(0) = -4sin(2*0) = 0

f''(0) = -8cos(2*0) = -8

f'''(0) = 16sin(2*0) = 0

f''''(0) = 32cos(2*0) = 32

Therefore, the first four nonzero terms of the Taylor series for f(x) = 4cos²(x) centered at a=0 are:

4 - 4x² + (8x⁴ / 4!) - (16x⁶ / 6!) + ...

Simplifying, we get:

4 - 2x² + (2x⁴ / 3) - (2x⁶ / 45) + ...

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Step-by-step explanation:

to find the percentage you have to take 5 as 100% so to find the percentage of 4 you have to divide 100 by 5 making 20%. then do 20 multiplied by 4 which is 80%. so the answer is 80^

Answer: 3237 photos

Step-by-step explanation:

Let the number of photos of size 3R that the school ordered be 'x', and the number of photos of size 6R be 'y'.

We know that the school ordered 308 photos of size 3R, so:

x = 308

We also know that the total amount spent on photos was Rs 18500, so:

3x + 6y = 18500

Substituting the value of x from the first equation:

3(308) + 6y = 18500

924 + 6y = 18500

6y = 17576

y = 2929.33 (rounded off to the nearest whole number)

Since the number of photos must be a whole number, we can assume that the school ordered 2929 photos of size 6R.

Therefore, the total number of photos that the school ordered together is:

x + y = 308 + 2929 = 3237

Hence, the school ordered a total of 3237 photos.

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The area of the regular polygon, or equilateral triangle, is determined as  27.71 mm².

The area of a regular polygon can be calculated using the formula:

Area = (perimeter * apothem) / 2

where;

Assuming the regular polygon is an equilateral triangle, the following formula will be used to find the area of the triangle.

A = a² × √3/4

where;

a is the side length of the  equilateral triangle = 8 mm

The area of the equilateral triangle is calculated as follows;

A = ( 8² ) x √ ( 3 ) / 4

A = 27.71 mm²

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Since the y-intercept of f(x)=4(3)ˣ is (0,4) and the y-intercept for the  table whose function is g(x) = 3²⁻ˣ is (0,9). See the attached graph. Hence, the function with the larger y-intercept is g(x) = 3²⁻ˣ.

In analytic geometry, a point where the graph of a given function or relation intersects with the y-axis of its coordinate system is known as the vertical intercept.

It obeys one standard convention: That all horizontals correspond to values on x and all verticals correspond to those on y. At these points, metrics assessing intersection require that x must always equal zero.

Hence, on the basis of the points at which the curve meets the y axis in  both graphs, we can correctly state that: the function with larger y-intercept is g(x) = 3²⁻ˣ.

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A painting contractor determined the average amount of time needed to paint a house.

- When 2 painters are used, it takes 15 hours to paint

- When 6 painters are used, it takes 5 hours to paint.

If p represents the number of painters and h represent the number of hours required to paint the house, which statement is true about this relationship?

F. The time required to paint a house varies directly with

the number of painters because h = 30p.

G. The time required to paint a house varies directly with

the number of painters because ph = 30.

H. The time required to paint a house varies inversely

with the number of painters because h = 30p.

J. The time required to paint a house varies inversely

with the number of painters because ph = 30.

Answer:

(7-2√6)/10

Step-by-step explanation:

I assumed the fraction in the question was:

(√6 - 1) / (2√6 + 2)

Working is attached below.

The series [tex]\lim_{n \to \infty} sin(n)[/tex] does not converge, because the function [tex]sin(n)[/tex] oscillates infinitely between -1 and 1 as n approaches infinity.

More formally, for any positive integer [tex]k[/tex], we can find an integer [tex]n[/tex] such that [tex]n\pi[/tex] is very close to [tex]\pi[/tex], which implies that [tex]sin(n)\approx(-1)^k[/tex]. Therefore, the sequence [tex]{sin(n)}[/tex] does not converge to any limit as [tex]n[/tex] approaches infinity.

Alternatively, we can also prove that [tex]\lim_{n \to \infty} sin(n)[/tex] does not exist using the epsilon-delta definition of a limit. Suppose there exists a limit [tex]L[/tex], then for any [tex]\epsilon > 0[/tex], there exists a positive integer [tex]N[/tex] such that for all [tex]n > N[/tex], we have [tex]|sin(n) - L| < \epsilon[/tex].

However, we can choose [tex]\epsilon = 1/2[/tex] and find two subsequences [tex]{a_n}[/tex] and [tex]{b_n}[/tex] such that [tex]|sin(a_n) - sin(b_n)| = 1[/tex]. Therefore, for any possible limit [tex]L[/tex], we can always find two subsequences that converge to different values, contradicting the assumption that the limit exists.

[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

♥️ [tex]{\underline{\underline{\textrm{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:}}}}}}\\[/tex]

The exponential function graphed is defined as follows:

y = 4(3)^x - 1.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function in this problem has an horizontal asymptote at y = -1, hence it is defined as follows:

y = ab^x - 1.

When x increases by one, y is multiplied by 3, hence the parameter b is given as follows:

b = 3.

Hence:

y = a(3)^x - 1.

When x = 0, y = 3, hence the parameter a is given as follows:

a - 1 = 3

a = 4.

Thus the function is:

y = 4(3)^x - 1.

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The 99.7% confidence interval for the mean of the population is (112.82, 125.18).

The degree of variance or dispersion in a collection of data is measured by standard deviation. It is a statistic that gauges how much values deviate from the dataset's mean (average).

To calculate the 99.7% confidence interval for the mean of the population, we need to use the formula:

Confidence Interval = X ± Z(α/2) * (σ/√n)

where:

X is the sample mean

Z(α/2) is the critical value of the standard normal distribution at α/2 level of significance (α is the level of significance)

σ is the population standard deviation (unknown)

n is the sample size

In this case, X = 119, σ = 16, n = 64, and α = 0.003 (because 99.7% corresponds to the area under the curve outside the range of ±3 standard deviations from the mean, and the standard normal distribution is symmetric around the mean, so we need to split the area of 0.003 equally between the two tails).

Using a standard normal distribution table or calculator, we find that Z(α/2) = Z(0.0015) = 3.090.

Plugging in the values, we get:

Confidence Interval = 119 ± 3.090 * (16/√64)

Confidence Interval = 119 ± 6.18

Therefore, the 99.7% confidence interval for the mean of the population is (112.82, 125.18).

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The total area of the entire space is 1728.72 feet².

We have,

From the figure,

It has 4 shapes:

Semicircle, Rectangle, trapezium, and a smaller rectangle.

Now,

Diameter of the semicircle = 4 units

Radius = 2 units = 2 x 7 = 14 feet

Area = 1/2 x π x r² = 1/2 x 3.14 x 14 x 14 = 307.72 feet²

And,

Area of the Rectangle.

= 5 units x 3 units

= 5 x 7 x 3 x 7

= 15 x 49

= 735 feet²

And,

Area of the trapezium.

= 1/2 x 1 unit x (3 units + 5 units)

= 1/2 x (1 x 7) x (8 x 7)

= 1/2 x 7 x 56

= 196 feet²

And,

Area of the rectangle.

= 5 units x 2 units

= 5 x 7 x 2 x 7

= 35 x 14

= 490 feet²

Now,

The total area of the entire space.

= 307.72 + 735 + 196 + 490

= 1728.72 feet²

Thus,

The total area of the entire space is 1728.72 feet².

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The value of the percentage 64% of 35 is 22.4

To find 64% of 35, we can use the following formula:

percent × whole = part

where percent is the percentage we want to find, whole is the total value, and part is the result we are looking for.

In this case, we want to find 64% of 35, which means that percent = 64 and whole = 35.

Let's substitute these values into the formula:

64% × 35 = part

To calculate the product of 64% and 35, we can convert 64% to a decimal by dividing it by 100:

64% ÷ 100 = 0.64

Substituting this value into the formula, we get:

0.64 × 35 = part

Multiplying 0.64 by 35, we get:

22.4 = part

Therefore, 64% of 35 is 22.4.

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The solution to the equation is [tex]? = 2/13[/tex] .

the variable (?) in order to solve this problem. By multiplying both sides by the fraction's denominator (2 and 1/2 or 5/2) we can first get rid of the fraction.

[tex](5/2) \times ? times 2[/tex]  and  [tex]1/2 = (5/2) \times 1/4[/tex]

Simplifying the left-hand side, we get:

[tex](5/2) \tmes ? times 2[/tex] and [tex]1/2 = (5/2) \times (5/2) \times 1/10[/tex]

Now, we can simplify the right-hand side:

[tex](5/2) \times ? \times 2 \ and\ 1/2 = 1/2[/tex]

Next, we need to get rid of the coefficient of ? by dividing both sides by  [tex](5/2) \times 2[/tex] and 1/2:

[tex][(5/2) ? \times 2[/tex]  and  [tex]1/2] / [(5/2) \times 2[/tex] and  [tex]1/2] = (1/2) / [(5/2) \times 2 and 1/2][/tex]

Simplifying the left-hand side, we get:

[tex]? = (1/2) / [(5/2) \times 2 and 1/2][/tex]

Now, we need to simplify the right-hand side:

[tex]? = (1/2) / (13/4)[/tex]

To divide by a fraction, we multiply by its reciprocal:

[tex]? = (1/2) \times (4/13)[/tex]

Simplifying the right-hand side, we get:

[tex]? = 2/13[/tex]

Therefore, the solution to the equation is   [tex]? = 2/13.[/tex]

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