The total difference between 4 5/6 and 9 1/6 on a number line using shorter jumps to the nearest integers is 4 1/3.
To find the difference between 4 5/6 and 9 1/6 on a number line using shorter jumps to the nearest integers, we can follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
4 5/6 = (6 x 4 + 5) / 6 = 29/6
9 1/6 = (6 x 9 + 1) / 6 = 55/6
Step 2: Find the distance between the two fractions on the number line by taking the absolute value of their difference.
|29/6 - 55/6| = |-26/6| = 26/6
Step 3: Simplify the fraction and convert it back to a mixed number, if necessary.
26/6 can be simplified to 13/3, which is an improper fraction.
To convert 13/3 back to a mixed number, we divide the numerator (13) by the denominator (3) and write the remainder as a fraction:
13 ÷ 3 = 4 with a remainder of 1
So, 13/3 = 4 1/3
Therefore, on a number line with shorter jumps to the nearest integers, the total distance between 4 5/6 and 9 1/6 is 4 1/3.
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Question 2-5 Use the following information to answer Part A and Part B. A population of birds can be represented by a quadratic function where t represents the time in months since the birds were first co birds. This function can be represented with three equivalent forms. Part A Inline Drop Down: 1 point for answer only mit Test B=-0.4(t+10)(1-350) B=-0.412+1361+1400 Which form reveals the number of birds present on the island when counting first started? B=-0.412+1361+140 B =
According to given c represents the initial number οf birds οn the island
What is a quadratic equatiοn?A pοlynοmial οf degree twο in οne οr mοre variables is referred tο as a quadratic pοlynοmial. The pοlynοmial functiοn that a quadratic pοlynοmial defines is knοwn as a quadratic functiοn.
functiοn represents a quadratic mοdel fοr the bird pοpulatiοn, we can write it in standard fοrm as:
f(t) = at² + bt + c
where a, b, and c are cοnstants.
Substituting t = 0 in the standard fοrm οf the quadratic functiοn, we get:
f(0) = a(0)² + b(0) + c
f(0) = c
Therefοre, the value οf c in the standard fοrm οf the quadratic functiοn represents the number οf birds present οn the island when cοunting first started.
Sο, the fοrm that reveals the number οf birds present οn the island when cοunting first started is the standard fοrm. f(t) = at²+ bt + c
where c represents the initial number οf birds οn the island.
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Find the measure of the missing angle and arc
It is important to carefully read and understand the information given in the problem, as well as to apply the appropriate formulas and properties to find the solution
Sure, I'll be happy to help you with your question. In order to find the measure of the missing angle and arc, we first need to know what type of angle and arc we are dealing with. If it is a central angle and arc, then the measure of the angle is equal to the measure of the arc. However, if it is an inscribed angle and arc, then the measure of the angle is half the measure of the arc.
Once we have determined the type of angle and arc, we can use the given information to solve for the missing measure. For example, if we are given the measure of the angle and the measure of the arc, we can use the formula for the measure of a central angle or inscribed angle to solve for the missing measure.
Alternatively, we can also use the properties of circles, such as the fact that the sum of the angles in a triangle is 180 degrees and the fact that the angle at the center of a circle is twice the angle at the circumference, to solve for the missing measure.
In any case, . With enough practice and familiarity with these concepts, you can become proficient at solving problems involving missing angles and arcs.
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Find the area of the Trapezoid
24mi
8.2mi
9 mi
9.7mi
please explain I'll mark brainlisest
Answer:
A = 46.74 mi²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{h}[/tex] (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 8.2 , b₁ = 9 , b₂ = 2.4
then
A = [tex]\frac{1}{2}[/tex] × 8.2 × (9 + 2.4) = 4.1 × 11.4 = 46.74 mi²
Please help I need these differential equations done by today and cannot do it.
the particular solution to the differential equation. we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]
What is the differential equation?To find the particular solution to the differential equation {dy}/{dx} = (x+1) (y+1) with the initial condition y(4) = 3, we can use separation of variables and integration.
First, we can rewrite the equation as:
[tex]{1}/{(y+1)} dy = (x+1) dx[/tex]
Next, we can integrate both sides:
[tex]∫ {1}/{(y+1)} dy = ∫ (x+1) dx[/tex]
[tex]ln|y+1| = 1/2 x^2 + x + C[/tex]
where C is the constant of integration.
To determine the value of C, we can use the initial condition y(4) = 3:
[tex]ln|3+1| = 1/2 (4)^2 + 4 + C[/tex]
[tex]ln|4| = 10 + C[/tex]
[tex]C = ln|4| - 10 = -5.605[/tex]
Therefore, the particular solution to the differential equation with the initial condition y(4) = 3 is:
[tex]ln|y+1| = 1/2 x^2 + x - 5.605[/tex]
Solving for y:
[tex]|y+1| = e^(1/2 x^2 + x - 5.605)[/tex]
[tex]y+1 = \pm e^(1/2 x^2 + x - 5.605)[/tex]
[tex]y = -1 \pm e^(1/2 x^2 + x - 5.605)[/tex]
Since [tex]y(4) = 3[/tex], we can determine which sign to use:
[tex]3 = -1 + e^(1/2 (4)^2 + 4 - 5.605)[/tex]
[tex]3 = -1 + e^(7.395)[/tex]
[tex]4 = e^(7.395)[/tex]
Therefore, we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]
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Please help and include scratch thank you.
Hence, the value of y is 23 when x = 7.
Describe equation?
A mathematical equation is a formula that uses the equals symbol (=) to denote the equality of two expressions.
A formula would be 3x - 5 = 16,
for instance. We may determine the value of the variable x by solving this equation: x = 73.
The slope-intercept representation of the equation can be used to determine the equation of a line running through the points (x1, y1) and (x2, y2):
y - y1 = m(x - x1) (x - x1)
where m is the line's slope. The following formula can be used to determine the line's slope:
m = (y2 - y1) / (x2 - x1) (x2 - x1)
Now put the x and y value in this:
slope of the line using the points (1, 5) and (3, 11):
m = (11 - 5) / (3 - 1) = 6 / 2 = 3
We can use the slope of the line to determine the equation of the line now that we know it:
y - y1 = m(x - x1) (x - x1)
y - 5 = 3(x - 1) (x - 1)
y - 5 = 3x - 3 = 3x + 2
In light of this, the equation for the line connecting points (1, 5) and (3, 11) is y=3x+2
To determine the value of y for x = 7, we can utilize the equation of the line we discovered earlier:
y = 3x + 2
y = 3(7) + 2
y = 21 + 2
y = **23**
Graph calculation given below:
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3 Seventy-two books were to be divided up among 18 children. Which of the following expressions are equivalent to this fraction? Select THREE that apply. A. 8 6 B. }+ 8 D. 2•7 E. F. 3.
72 books were divided up among 18 children means 18 kids and 72 books equal 4 books for each youngster.
What is a fraction?An element of a whole is a portion. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a straightforward fraction. A fraction appears in the numerator or denominator of a complicated fraction. The numerator of a perfect fraction is less than the denominator.0
1) 8/3 split by 6/9: To begin, we divide both the numerator and denominator by 3 to reduce 6/9 to 2/3.
8/3 ÷ 2/3 = (8/3) x (3/2) = 4
The fraction we began with is not equivalent to this expression.
2) 8/3 times 2/3: By multiplying the numerators and denominators, we can reduce this expression:
(8/3) x (2/3) = 16/9
The fraction we began with is not equivalent to this expression.
3) 2/9 split by 8/9: We multiply the first fraction by the reciprocal of the second fraction to divide fractions:
(2/9) ÷ (8/9) = (2/9) x (9/8) = 1/4
The fraction we began with is not equivalent to this expression.
4) In order to simplify this equation, let's first reduce 8/2 to 4:
2 x 4 = 8
The fraction we began with is not equivalent to this expression.
The fraction that accurately describes the circumstance cannot be expressed using any of the given expressions.
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round to the nearest tenth 16 37 =x
The value of x in the given right triangle can be found with help of trigonometric-ratios, given an angle 16° and hypotenuse 37 units is 35.566657. On rounding off to nearest tenths we get 35.6 units.
What are trigonometric-ratios?
In a given right triangle, the ratios of different sides are represented as six trigonometric ratios which are cosine,sine,cosecant,cot,secant and tan.
Sin of an angle=[tex]\frac{side opposite to the angle}{hypotenuse of triangle}[/tex]
Cosine of an angle=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]
tan of an angle= [tex]\frac{side opposite to the angle}{side adjacent to the angle}[/tex]
And cosecant, secant and cot are the reciprocals of sine, cosine & tan respectively.
Here,on naming the given right triangle we can see that
∠A = 16° , AC=37 units and Side AB= x units
Applying cosine of angle 16°, we get
cos A=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]
Cos 16°=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]
Cos 16°= [tex]\frac{AB}{AC}[/tex]
0.961261= [tex]\frac{AB}{AC}[/tex] {Cos 16°=0.961261}
0.961261=[tex]\frac{x}{37}[/tex] {AB=x and AC=37}
x = 0.961261 (37)
x = 35.566657
On rounding off to nearest tenths x=35.6 units
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Refer to the attachment for complete question & naming of triangle.
If <1 and <2 are vertical angles and m<22 = 180°, find m<1
If ∠1 and ∠2 are vertical angles and m∠22 = 180°, then m∠1 = 90°
Vertical angles are pairs of angles that are opposite to each other when two lines intersect. Vertical angles are always equal in measure. Therefore, if ∠1 and ∠2 are vertical angles, then:
∠1 = ∠2
We are also given that m∠22 has a measure of 180°. Since ∠1 and ∠2 are vertical angles, they form a straight line, and their measures add up to 180°. Therefore:
∠1 + ∠2 = 180°
Since ∠1 = ∠2, we can substitute ∠1 for ∠2 in the above equation:
∠1 + ∠1 = 180°
Simplifying the equation, we get:
2∠1 = 180°
Dividing both sides by 2, we get:
∠1 = 90°
Therefore, ∠1 has a measure of 90°.
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What is the value of x that represents the solution to the equation below? 51x – 19.5 = 108
Answer:
2.5
Step-by-step explanation:
51x - 19.5 + 19.5 = 108 + 19.5
51x = 127.5
x = 127.5/51
= 2.5
a survey asks teachers and students whether they would like the new school mascot to be a viking or a patriot. this table shows the results. which statement is true
Answer:
Option D.
Step-by-step explanation:
According to this survey results:
Students: 80 like viking and 20 like patriot.
Teachers: 5 like viking and 15 like patriot.
In Option A it is given that patriot is more popular in students while viking is more popular in teachers which is not correct.
In option C patriot is equally popular in students and teachers, which is also not correct. because patriot is popular in 20% of students but 80% in teachers, which is not correct.
In option B there is no difference between students and teachers, this statement is also not correct because there is lots of differences in their choices.
In Option D it is said that viking is more popular in students but patriot is more popular in teachers. this is correct.
stratified random sampling is a method of selecting a sample in which . a. the population is first divided into groups, and then random samples are drawn from each group b. the elements are selected on the basis of convenience c. various strata are selected from the sample
The stratified random sampling is a method of various strata are selected from the sample. So, the right choice for answer is option(c).
The four probability sampling methods mainly applied in research methods include simple random sampling, cluster sampling, stratified sampling, and systematic sampling. In certain situations, we need to remove the sampling bias, and for that, we opt for stratified random sampling. Here we talking about stratified random sampling. A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub populations) and random samples are drawn from each. Therefore, the required choice is option (c), that is various strata are selected from the sample.
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16^3 similar expressions
Answer: 2^12
4^6
64^2
the cube root of 4,096
256 times 2
8^6
65,536/4
16 times 16 times 16
256 cubed root of 256
256/16^4
64 times 4 times 2
Step-by-step explanation: All of these expressions are equal to 16 cubed, which is 4,096.
Answer:
4096 have a nice day
Step-by-step explanation:
pl z mark me brianliest :)
the variance of a sample of 144 observations equals 576. the standard deviation of the sample equals group of answer choices 12. 63,504. 21. 441.
The sample's standard deviation is equal to 12. Thus, choice B is the right choice.
The variance of a sample of 144 observations equals 576.
Variance S² = 144
The standard deviation is a measure of how spread out a set of data is. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
The standard deviation can be used to measure the amount of variation or dispersion of a set of data values from the mean.
Standard Deviation = √Variance
Standard Deviation = √144
Standard Deviation = 12
The standard deviation of the sample equals 12. So the option B is correct.
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The complete question is:
The variance of a sample of 144 observations equals 576. The standard deviation of the sample equals:
A. 441
B. 12
C. 63,504
D. 21
a national survey reported that 35% of adults in a certain country have hypertension a sample of 25 adults is studied what is the mean number of adults who have hypertension
The mean number of adults who have hypertension in a sample of 25 adults is 8.75, assuming the national survey-reported percentage of adults with hypertension (35%) applies to the sample.
The mean number of adults who have hypertension in the sample of 25 can be calculated by multiplying the sample size (25) by the population proportion (0.35). Mathematically,
Mean = n * p = 25 * 0.35 = 8.75
Therefore, the mean number of adults who have hypertension in the sample is 8.75. Note that this is an expected value and there may be variability around this mean in different samples.
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which statement about a quadrilateral is true? responses a rhombus has exactly one pair of parallel sides. a rhombus has exactly one pair of parallel sides. a trapezoid has two pairs of parallel sides. a trapezoid has two pairs of parallel sides. all rectangles are squares. all rectangles are squares. some rhombuses have four right angles.
The statement that is true about rhombus is d. some rhombuses have four right angles.
A rhombus is a parallelogram with equal-length sides, though the angles at the opposing ends need not be equal, nor must the sides be parallel. If a rhombus is also a cube, it can have four right angles. It can be viewed as an equal-sided trapezoid as well.
A parallelogram has two sets of parallel sides, whereas a trapezoid only has one pair of parallel sides. Therefore, it is untrue that a trapezoid has two sets of parallel edges. Not all rectangles are squares, but they are all quadrilaterals with four right angles. A unique variety of parallelogram called a square has equal-length edges. Therefore, it is untrue to say that all circles are squares.
Complete Question:
which statement about a quadrilateral is true?
a. a rhombus has exactly one pair of parallel sides.
b. a trapezoid has two pairs of parallel sides.
c. all rectangles are squares.
d. some rhombuses have four right angles.
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lester jarred 30 liters of jam after 3 days. how many does lester need to spend making jam if he wants jar 40 liters of jam in all? solve using unit rates
Thus, it will take 4 days time for the Lester to spend on preparing the jar of 40 liters of jam.
Explain about the proportion of numbers:If we were to assume that we had any two quantities (as well as 2 entities) and that we were tasked with figuring out their ratio, the ratio formula would be defined as a: where b = a/b
Any two numbers could constitute a and b.The initial term or antecedent is "a."The second phrase or consequent is "b."Given data:
Time to jam 30 liters ---> 3 days.
Time to jam 40 litres ---> x days (say)
Then, taking the proportion,
30 lit / 3 day = 40 lit / x days
x = 3*40 / 30 days
x = 4 days
Thus, it will take 4 days for the Lester to spend on preparing the jar of 40 liters of jam.
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evaluate the triple integral. f 1 dv where f = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4 − x2 , 0 ≤ z ≤ 4 − x2 }
The triple integral evaluates to 8/15.
Evaluate the triple integral?To evaluate the triple integral f 1 dv where f = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4 − x^2, 0 ≤ z ≤ 4 − x²},
Set up the triple integral
The triple integral is written as ∭(1) dV, with the limits of integration for x, y, and z as given in the problem.
Integrate with respect to z
∫(∫(∫(1) dz) dy) dx
The limits for z are 0 to 4-x², so integrate with respect to z:
∫(∫[(z)|from 0 to 4-x²] dy) dx
Substitute the limits for z
∫(∫[(4-x²)] dy) dx
Integrate with respect to y
∫[(4-x²)y|from 0 to 4-x²] dx
Substitute the limits for y
∫[(4-x²)²] dx
Integrate with respect to x
Integrate the function with respect to x:
∫(16 - 16x² + x⁴) dx from 0 to 2
Substitute the limits for x
[4x³/3 - 16x³/3 + x⁵/5]|
from 0 to 2
Calculate the final result
(4(2)³/3 - 16(2)³/3 + (2)⁵/5) - (0) = (32/3 - 128/3 + 32/5) = 8/15
So, the triple integral evaluates to 8/15.
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An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $5800 and her stock in Company B was worth $7470. The stock in Company A has decreased 1% since last year and the stock in Company B has decreased 20%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
To find the total percentage decrease, we first need to find the new values of the stocks in Company A and Company B after the decrease.
The new value of the stock in Company A is: $5800 - (1% \times $5800) = $5742
The new value of the stock in Company B is: $7470 - (20% \times $7470) = $5976
To find the total value after the decrease, we add these two values: $5742 + $5976 = $11718
To find the percentage decrease from the original total value ($5800 + $7470 = $13270) to the new total value ($11718), we use the formula:
percentage decrease = [(original value - new value) / original value] x 100%
percentage decrease = [($13270 - $11718) / $13270] x 100%
percentage decrease = 11.7%
Therefore, the total percentage decrease in the investor's stock account is 11.7%.
Jason goes to the sandwich shop for lunch. The prices for sandwiches are listed below.
What number completes the number sentence 3m = ?
2g
3g
4g
5g
The number completes the number sentence 3m= 5g.
What number completes the number sentence 3m = ?The m refers the meatball which prices $2.50
so for 3m = 3*2.50
3m = $7.5
g refers to grilled cheese which prices $1.50
so we have to find for how many grilled cheese which equals $7.5
On dividing we get, 7.5/1.50 = 5
Hence 3 meatballs equal 5 grilled cheese, 3m = 5g
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what reflection occurred? Explain please.
The reflection that occurred is over the x-axis.
EquationsBased on the given coordinates, it can be observed that each point of the pre-image was reflected over the x-axis, resulting in a new image. Therefore, the type of reflection that occurred is a reflection over the x-axis.
To explain this with equations, we can use the transformation formula for a reflection over the x-axis:
(x, y) → (x, -y)
Using this formula, we can find the image coordinates of the pre-image points:
A' = (-1, -8)
B' = (5, 3)
C' = (-5, 1)
As we can see, the y-coordinates of each point have been negated, indicating a reflection over the x-axis. Therefore, the type of reflection that occurred is a reflection over the x-axis.
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in the last 10 softball games delisa has scored the following number of runs for her team: 2, 1, 3, 3, 1, 3, 2, 4, 3, 5. the mode number of runs for delisa would be:
In the last 10 softball games, the mode number of runs for Delisa is 3.
Mode is the value that appears most frequently in a given data set. It is one of the three measures of central tendency, along with mean and median.
To find the mode, we need to determine which number appears most frequently in the data set. In this case, the number of runs that Delisa scored in each game.
We have been given the data points,
2,1,3,3,1,3,2,4,3,5
The number 3 appears most frequently, occurring three times. Therefore, the mode number of runs for Delisa is 3.
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PLEASE HELPP
Linus wants to have 500 copies of his resume printed. His local print shop charges $18.50 for the first 200 copies and $9 for every 100 additional copies. How much will the 500 copies cost?
A)$46.25
B)$45.50
C)$45.00
D)$46.00
A Christmas promotion included a $2.5 mail-in rebate for the purchase of a 10-liter bottle of milk and a store coupon for $1.39 off a 5-liter bottle of vegetable oil. Jesse Gatling bought one 10-liter bottle of milk for for $33.00 and a 5liter bottle of vegetables oil for $26.89. Calculate his total cost if an envelope costs $0.10 and a stamp costs $0.28
Answer:
can u break that down
Step-by-step explanation:
A rectangular prism has a base area of 54 m (to the 2nd power) and a volume of 702 m (to the 3rd power). What is its height?
Answer:
13 meters.
Step-by-step explanation:
We can use the formula for the volume of a rectangular prism, which is:
Volume = length x width x height
We are given that the base area (length x width) of the prism is 54 m², so we can write:
length x width = 54 m²
We are also given that the volume of the prism is 702 m³, so we can write:
Volume = length x width x height = 702 m³
We want to find the height of the prism, so we can rearrange the formula for the volume to solve for height:
height = Volume / (length x width)
Substituting the given values, we get:
height = 702 m³ / 54 m²
Simplifying this expression, we can divide both the numerator and the denominator by the greatest common factor of 54 and 702, which is 18:
height = (702/18) m / (54/18) m = 39 m / 3 m
height = 13 meters
Therefore, the height of the rectangular prism is 13 meters.
Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by σ=29lb.
(a) If 1 woman is randomly selected, find the probabity that her weight is above
176
(b) If 4 women are randomly selected, find the probability that they have a mean weight above 176
(c) If 57women are randomly selected, find the probability that they have a mean weight above 176
Answer:
a) 0.128 b) 0.51 c) 7.27
Step-by-step explanation:
a)
Lower Bound: 176
Upper Bound: 99999
μ: 143
σ: 29
= 0.1275….
b)
Lower Bound: 176
Upper Bound: 99999
μ: 143
σ: 29
0.1275… (4) = 0.51
c)
Lower Bound: 176
Upper Bound: 99999
μ: 143
σ: 29
0.1275… (57) = 7.27
4. if an athlete eats a large meal before a competition, how many hours before the competition should she finish eating? a. 1 hour b. 1.5 hours c. 2 hours d. 2.5 hours e. 3 hours
Option D is the correct option i.e., 2.5 hours. Timing is everything when it comes to dining before a fight. Athletes must ingest enough calories to power their efforts without developing gastrointestinal pain or bloating while competing. Typically, a substantial dinner should be eaten two to three hours prior to the game.
The body needs time to process and assimilate nutrients, which is the cause of this. A big dinner requires the body to divert a lot of blood flow to the digestive system, which can have an impact on an athlete's performance. Athletes' performance can be hampered by sluggishness, gastrointestinal pain, or even vomiting brought on by eating too close to a competition.
In general, it is recommended that athletes experiment with different meal timings and types of food during their training to determine what works best for their individual needs.
They should also consider the length of the event and the intensity of their activity to determine the amount and timing of their meals. A registered dietitian or sports nutritionist can help athletes create a personalized nutrition plan to optimize their performance.
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If a function is defined as f(x)=2x+3 , find the value of f(4
Answer: f(4) = 11
Step-by-step explanation: See image below.
Answer: 11
Step-by-step explanation:
you need to put 4 where the X is: f(4)=(2*4)+3 = 11
Question 4 of 10
The graph of F(x), shown below, resembles the graph of G(x)=x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Answer: The answer is C, f(x) = 2x^2 + 3.
Step-by-step explanation: Check the graph below.
b. Use function notation to write a rule
that defines function r.
c. On the coordinate plane, sketch a
graph of function r.
d. Solve the equation r(u) = 30 and
explain what the solution means in
this situation.
Using functions,
a) 1. 48
2. 21
3. 75 - 4.5w
b) r = 75 - 4.5w
c) Graph is attached.
d) The restaurant has 30kgs of rice after 10 weeks.
Define a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here as per the question,
a)
1. 75 - (4.5 × 6)
= 75 - 27
= 48
2. 75 - (4.5 × 12)
= 75 - 54
= 21
3. 75 - (4.5 × w)
= 75 - 4.5w
b)
r = 75 - 4.5w
c) Image is attached for the graph.
d) 30 = 75 - 4.5w
Subtracting both sides by 30:
⇒ 0 = 75 - 4.5w - 30
Adding both sides by 4.5w:
⇒ 4.5w = 75 - 30
⇒ 4.5w = 45
Dividing both sides by 4.5:
⇒ w = 45/4.5
⇒ w = 10.
Therefore, the restaurant has 30kgs of rice after 10 weeks.
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The complete question is:
b. Use function notation to write a rule
that defines function r.
c. On the coordinate plane, sketch a
graph of function r.
d. Solve the equation r(u) = 30 and
explain what the solution means in
this situation.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
Correct options are A, B, E--------------------------
Standard form for the equation of a circle is:
(x − h)² + (y − k)² = r², where (h, k) is the center and r is the radiusConvert the given equation into standard form:
x² + y² - 2x - 8 = 0x² - 2x + 1 + y² - 9 = 0(x - 1)² + y² = 9(x - 1)² + y² = 3²Its center is ( 1, 0) and radius is r = 3.
Let's verify the statements:
A) The radius of the circle is 3 units - TRUE, r = 3;B) The center of the circle lies on the x-axis - TRUE, point (1, 0) is on the x-axis;C) The center of the circle lies on the y-axis - FALSE, the x- coordinate of the center is not zero; D) The standard form of the equation is (x – 1)² + y² = 3 - FALSE, r²= 9 but not 3;E) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9, TRUE, its radius is r² = 9 ⇒ r = 3.Answer:
See below
Step-by-step explanation:
To find:-
Which statements are true .Answer:-
The given equation of the circle is ,
[tex]\longrightarrow x^2+y^2-2x-8 = 0 \\[/tex]
For finding the correct statements , we need to convert this equation into standard form for a circle.
The standard equation of circle is given by,
[tex]\boxed{\begin{tabular}{c}\textbf{\underline{ \red{Standard\ equation\ of \ circle }}} \\ \\ \text{ The standard equation of a circle is given by:-} \\\\ \longrightarrow \underline{\underline{ (x-h)^2+(y-k)^2 = r {}^{2}}} \\\\ \text{where} , \\\\ \bullet\text{ (h,k) is the centre of the circle.}\\\\\bullet\text{ "r" is the radius of the circle. }\\\end{tabular}}[/tex]
Now for that we need to complete the square for "x" . This can be done by ,
Rearrange the terms,
[tex]\longrightarrow x^2-2x + y^2-8 = 0 \\[/tex]
Add and subtract 1² .
[tex]\longrightarrow ( x^2 -2x +1^2 ) - 1^2 + y^2-8=0 \\[/tex]
Simplify,
[tex]\longrightarrow (x^2-2(1)x+1^2) - 1-8 + y^2=0 \\[/tex]
Notice that the terms inside the small brackets are in the form of a² - 2ab + b² , which is the whole square of (a-b) . So we can write it as,
[tex]\longrightarrow (x-1)^2 +y^2 - 9 = 0 \\[/tex]
Add 9 on both the sides ,
[tex]\longrightarrow (x-1)^2 + y^2 = 9\\[/tex]
This can be written as,
[tex]\longrightarrow \underline{\underline{ \boldsymbol{(x-1)^2+(y-0)^2 = 3^2}}} \\[/tex]
On comparing it to the standard form, we have;
[tex]\longrightarrow\boxed{ \text{Center = (1,0) }} \\[/tex]
[tex]\longrightarrow\boxed{ \text{ Radius = 3 \ units}} \\[/tex]
Let's check the given statements ,
Statement 1: The radius of the circle is 3 units.
This statement is true as we just calculated the radius to be 3 units.Statement 2: The centre of the circle lies on the x-axis.
This statement is also true as you can see that the y coordinate to the centre is 0 , and the x coordinate is 1 , so it will be on x-axis .Statement 3: The statement of the circle lies on the y-axis.
This statement is false since in the previous statement we proved that the centre lies on the x-axis .Statement 4: The standard equation of the circle is (x-1)²+y² = 3
This statement is false as we calculated the value of r² to be 9 .Statement 5: The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The given equation of circle is x² + y² = 9 , if we convert this into standard form, we will get ; x² + y² = 3² . Now on comparing it to the standard equation, we see that the radius is 3 units . Hence the given statement is also true .The graph for the same has been attached.