The pie charts below show information about the animals that were treated in a veterinary surgery during one weekend. 300 animals were treated on Saturday. 125 animals were treated on Sunday. What percentage of all the animals treated during the weekend were tortoises? Give your answer to the nearest 1%. 22% 19% Saturday 3% 56% Animals treated Sunday 4% 48% 28% 12% 8% Key Tortoise Rabbit Cat Dog Hamster Not drawn accurately​

Answer:

y=2

Step-by-step explanation:

The equation of a parabola in the form [tex](y-k)^2=4p(x-h)[/tex] has an axis of symmetry of [tex]y=k[/tex]. Therefore, the axis of symmetry is [tex]y=2[/tex].

Answer:

y = 2

Step-by-step explanation:

The axis of symmetry of a parabola is a line that divides the parabolic curve into two symmetric halves. It is a line of symmetry that passes through the vertex of the parabola.

Given equation of the parabola:

[tex](y-2)^2=20(x+1)[/tex]

As the y-variable is squared, the given parabola is horizontal (sideways).

The standard form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

Comparing the given equation with the standard equation, we can see that:

As the axis of symmetry is given by the formula y = k, the axis of symmetry of the given parabola is y = 2.

Answer: -15/17

Step-by-step explanation:

sin ∅ = 8/17

If you drew a a line in the 2rd quadrant because tan ∅ <0, which means tan∅ is negative.

Tan∅= sin∅/cos∅            

they told you sin∅ is positive which is related to your y.

but cos∅ needs to be negative which is related to x

This happens in the second quadrant x is negative and y is positive.

Now we know which way to draw our line.  Label the opposite of the angle 8 and the hypotenuse 17 because sin∅ = 8/17

Use pythagorean to find adjacent.

17² = 8² + a²

225 = a²

a = 15

The adjacent is negative because the adjacent is on the x-axis in the negative direction.

cos ∅ = adj/hyp

cos∅ =  -15/17

Answer: -15/17

Step-by-step explanation:

In the first quadrant, all sine, cosine and tan are all positive. In the second quadrant, only sine is positive. Third quadrant, only tangent is positive and fourth quadrant, only cosine is positive.

Therefore, when sine is positive and tan is negative, the angle can only be in quadrant 2. Then draw the triangle. Draw a triangle with the angle from the origin, with the opposite leg from the angle with value of 8 and the hypotenuse of value 17. Since cosine is what the question is asking for, and we know the data given forms an right triangle, the value of the other leg is 15. It is an 8-15-17 special triangle or use the Pythagorean Theorem.

Finally, taking the cosine of the angle from the origin gives -15/17 since it is in quadrant 2.

Step-by-step explanation:

a number consists of digits in the place of certain values of the powers of 10.

2013 consists of a digit 2 in the thousands units position.

of a digit 0 in the hundreds units position.

of a digit 1 in the tens units position.

and of a digit 3 in the (single) units position.

so, to which power do we need to have this 3 ?

I think you made a mistake there. you say we need it to the power of 2013 ?

3²⁰¹³ = 2.786671338...e960 =

= 2.786671338... × 10⁹⁶⁰

The probability of Lashonda winning a prize is 9/11.

To find the probability of Lashonda winning a prize, we can use the odds given. The odds in favor of Lashonda winning a prize are expressed as 9/2.

Odds are typically represented as a ratio of favorable outcomes to unfavorable outcomes.

In this case, the favorable outcomes are Lashonda winning a prize, and the unfavorable outcomes are Lashonda not winning a prize.

The odds in favor of Lashonda winning a prize can be written as 9:2, where 9 represents the favorable outcomes and 2 represents the unfavorable outcomes.

To calculate the probability, we add the favorable and unfavorable outcomes to get the total number of possible outcomes.

In this case, the total number of outcomes is 9 + 2 = 11.

The probability of Lashonda winning a prize can be calculated as the ratio of the favorable outcomes to the total number of outcomes:

Probability = Favorable outcomes / Total outcomes

Probability = 9 / 11.

Therefore, the probability of Lashonda winning a prize is 9/11.

In conclusion, based on the given odds in favor of Lashonda winning a prize being 9/2, the probability of Lashonda winning a prize is 9/11.

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The ray or segment that is a chord is (d) segment FC

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

The circle

By definition, a chord is a straight line that joins points of the circle without passing through the center

The ray that has the above properties is ray FC

Hence, the segments that is a chord is (d) FC

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Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.

To calculate the population size after 4 hours, we can use the formula for exponential growth:

Population size = Initial population * [tex](1 + growth rate)^t^i^m^e[/tex]

Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:

Population size = 3.3 million *[tex](1 + 0.4465)^4[/tex]

Calculating the exponent first:

[tex](1 + 0.4465)^4 = 1.4465^4[/tex] ≈ 1.7879

Now, we can substitute this value back into the formula:

Population size = 3.3 million * 1.7879

Calculating the population size:

Population size = 5.892 million

Therefore, the population size after 4 hours is approximately 5.892 million cells.

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-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

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The length of this line segment is: B. 2√13 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(4 + 2)² + (1 + 3)²]

Distance = √[(6)² + (4)²]

Distance = √[36 + 16]

Distance = √52

Distance = 2√13 units.

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The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.

The integral of f(x) = ex - e with respect to x can be computed as follows:

∫[0, 2] (ex - e) dx

Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:

∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx

Integrating each term separately:

= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2

= (e2 - e0) - (e0 - e0)

= e2 - 1

The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

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Answer:

height = 10 ft

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

given A = 70 and b = 14 , then

[tex]\frac{1}{2}[/tex] × 14 × h = 70

7h = 70 ( divide both sides by 7 )

h = 10 ft

Answer:

That Platonic solid is a dodecahedron.

B is the correct answer.

The coterminal of 4π/3 angle measure are 10π/3 and -2π/3

We add or subtract integer multiples of 2π.

So, 4π/3 + 2π = 10π/3 is one coterminal angle, and

4π/3 - 2π = -2π/3 is another coterminal angle.

To convert 125.67° to degree, minute, and second measure:

125.67° = 125° + 0.67°

Since there are 60 minutes in 1 degree, we can multiply 0.67 by 60 to get the minutes:

0.67° × 60 = 40.2'

Since there are 60 seconds in 1 minute, we can multiply 0.2 by 60 to get the seconds:

0.2' × 60 = 12"

So, 125.67° is equivalent to 125° 40.2' 12".

To find the degree measure equivalent to 10π/13 rounded to the nearest hundredth of a degree, we can divide 10π/13 by π and then multiply by 180° to convert from radians to degrees:

(10π/13) / π * 180° ≈ 138.46° (rounded to the nearest hundredth).

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Answer: 140

Step-by-step explanation: 120-(-20) to 120 + 20 goes to 140.

The simplified fraction of 350/120 is 35/12

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

350/120

Divide the zeros

So, we have

350/120 = 35/12

Divide the fractions by 3

This is impossible

Hence, the simplified fraction is 35/12

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Answer:

the radius of the cylinder is approximately 2.26 feet.

Step-by-step explanation:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given that the volume is 400 feet, the height is 25 feet, and using π ≈ 3.14, we can rearrange the formula to solve for the radius:

400 = 3.14 * radius^2 * 25

Divide both sides of the equation by (3.14 * 25):

400 / (3.14 * 25) = radius^2

Simplifying:

400 / 78.5 ≈ radius^2

5.09 ≈ radius^2

To find the radius, we take the square root of both sides:

√5.09 ≈ √(radius^2)

2.26 ≈ radius

Rounding to the nearest hundredth, the radius of the cylinder is approximately 2.26 feet.

Answer:

Step-by-step explanation:

Volume Formula for a cylinder is  V=πr²h

Substitute the following:    400 = 3.14(r²)(25)

r=[tex]\sqrt{\frac{V}{\pi h} }[/tex]

r=[tex]\sqrt{\frac{400}{\pi 25} }[/tex]

r≈2.25676ft

For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.

B: They have a law of formation:

A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.

This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.

C: They are ordered:

In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.

Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.

A: They may or may not be infinite:

Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.

On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.

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Note: the translated question is:

To have a sequence it is essential that the numbers that form it:

A: be infinite

B: they have a law of formation C: they are ordered

Answer:

In the given equation, V(r) represents the volume of the air inside a basketball when the radius of the basketball is r.

Step-by-step explanation:

The function V(r) represents the volume of the basketball when the radius is r. So, the correct interpretation is that V(r) represents "the volume of the basketball when the radius is r."

Step-by-step explanation:

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon

The slope of 0.75 corresponds to option 3. So, the correct answer is 3) 0.75.

To find the slope, we can use the formula for the slope of a line:

slope (m) = (change in y) / (change in x)

In this case, x represents the number of miles to the destination and y represents the total cost of the load.

Given that the charge to deliver a load 40 miles is $280 and the charge to deliver a load 56 miles is $292, we can set up two points on the line: (40, 280) and (56, 292).

Now let's calculate the change in y and change in x:

Change in y = 292 - 280 = 12

Change in x = 56 - 40 = 16

Plugging these values into the slope formula:

slope (m) = (change in y) / (change in x) = 12 / 16 = 0.75

Therefore, the slope of the line representing the relationship between the number of miles (x) and the total cost of the load (y) is 0.75.

Option 3 is correct.

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1. the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, x = 9

2. In linear equation 4(3x + 5) - 3 = 9x - 7, x = -8

3. the linear equation 1/3(5x - 9) = 2(1/3x + 6), x = 15

A linear equation is an equation in only on variable.

1. To solve the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, we proceed as follows

5(x + 7) - 3(x - 4) = 7x + 2

Expanding the brackets, we have

5x + 35 - 3x + 12 = 7x + 2

Collecting like terms in the expression, we have

5x + 35 - 3x + 12 = 7x + 2

5x - 3x - 7x = 2 - 35 - 12

-5x = -45

x = -45/-5

x = 9

2. To solve linear equation 4(3x + 5) - 3 = 9x - 7, we proceed as follows

4(3x + 5) - 3 = 9x - 7

Expanding the brackets, we have

12x + 20 - 3 = 9x - 7

Collecting like terms in the expression, we have

12x - 9x = - 7 + 3 - 20

3x = -24

x = -24/3

x = -8

3. To solve  the linear equation 1/3(5x - 9) = 2(1/3x + 6), we proceed as follows

1/3(5x - 9) = 2(1/3x + 6)

Expanding the brackets, we have

5x/3 - 3 = 2/3x + 12

Collecting like terms, we have

5x/3 - 2x/3 = 12 + 3

3x/3 = 15

x = 15

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Answer:

Step-by-step explanation:

39 !!!!!

The exact volume of a cone with the same dimensions is 9428.57 cubic inches

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

The cylinder

The volume of the cone with the same dimensions is calculated as

Volume = 1/3 * Volume of cylinder

So, we have

Volume = 1/3 * 22/7 * (30/2) * (30/2) * 40

Evaluate

Volume = 9428.57

Hence, the exact volume of a cone with the same dimensions is 9428.57 cubic inches

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Sampling based upon equal probability is called d. Simple random sampling. The correct answer is d. Simple random sampling.

Simple random sampling is a sampling technique where each individual in the population has an equal probability of being selected for the sample. It is based on the principle of equal probability, ensuring that every element has the same chance of being chosen. This method involves randomly selecting samples without any specific grouping or stratification.

Cluster sampling involves dividing the population into clusters or groups and randomly selecting entire clusters for inclusion in the sample. It does not guarantee equal probability for individual units within each cluster.

Probability sampling is a general term that encompasses different sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. It refers to sampling techniques that rely on random selection and allow for the calculation of probabilities associated with sample estimates.

Stratified random sampling involves dividing the population into distinct strata based on certain characteristics and then selecting samples from each stratum in proportion to their representation in the population. It does not guarantee equal probability of selection for all individuals.

Systematic sampling involves selecting every kth individual from a population list after randomly selecting a starting point. It does not guarantee equal probability of selection for all individuals.

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The value of cos E in the triangle is √2/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.

Some of the trigonometric functions are ;

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.

Therefore;

cos E = 5/5√2

cos E = 1/√2

rationalizing the value;

cos E = √2/2

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The speed of the boat in water without a current is 15 miles per hour

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

Current of river = 4 miles per hour

Distance travelled = 209 miles

Time = 30 hours.

Represent the speed with x

So, we have

Next, we have

Time = Speed/Distance

So, we have

209/(x - 4) + 209/(x + 4) = 30

When evaluated, we have

x = 15

Hence, the speed is 15 miles per hour

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We can solve for the missing elements as follows:

1. Radius - 10 inches

Diameter - 20

Circumference -  62.8

Area - 314

2.  Radius  - 6ft

Diameter - 12

Circumference - 37.68

Area - 113.04

3.  Radius - 18

Diameter - 36 yards

Circumference - 113.04

Area - 1017.36

4.  Radius 15

Diameter - 30 cm

Circumference 94.2

Area - 706.5

5.  Radius - 5 mm

Diameter 10

Circumference 31.4

Area -78.5

6. Radius 20

Diameter - 40 inches

Circumference  125.6

Area -1256

To solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:

1. radius = 10 inches

diameter = 20

circumference = 2pie*r 2 *3.14*10 = 62.8

Area = 314

2. radius = 6ft

diameter = 12

circumference = 37.68

Area = 113.04

3. radius = 18

diameter = 36 yards

circumference = 113.04

Area = 1017.36

4. radius = 15

diameter = 30 cm

circumference = 94.2

Area = 706.5

5. radius = 5 mm

diameter = 10

circumference = 31.4

Area = 78.5

6. radius = 20 inches

diameter = 40 inches

circumference = 125.6

area = 1256

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Triangle PQR is similar to triangle P”Q”R” because the rotation and dilation transformations preserve the shape and angles of the original triangle.

The rotation simply changes the orientation of the triangle, but the angles and side lengths remain the same. The dilation scales all the side lengths by a factor of 9, which preserves the ratios of the side lengths and the angles of the original triangle.

Since similarity of two triangles is defined as the correspondence between the angles of one triangle to the angles of another triangle, and the ratio of the lengths of the corresponding sides is constant, PQR is similar to P”Q”R” because the angles of PQR and P”Q”R” are congruent, and the ratio of the lengths of the corresponding sides is the same. This means that PQR and P”Q”R” have the same shape and are therefore similar.

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Answer:

113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06

314.16-201.06=113.1