in july, clare rode her bike 15 miles in 72 minutes, at her constant speed. a how long did it take her to ride 10 miles? show or explain your thinking. quizzes

A statement about the data which must be true include the following: A. The spread from the lower quartile to the median is greater than the spread from the median to the upper quartile.

In Mathematics, a box plot is a type of chart that is used for the graphical or visual representation of the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided above, the five-number summary for the given data set include the following:

Spread from lower quartile (first) to median = 7 -4  = 3

Spread from median to upper quartile (third) =  9 - 7 = 2

Therefore, the spread from lower quartile (first) to median is greater than the spread from median to upper quartile (third).

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296 hot lunches were sold on Friday.

The number of hot lunches sold on Friday can be calculated by multiplying the total number of hot lunches by the relative frequency on Friday:

Hot lunches sold on Friday = 1,350 * 0.22 = 296

Relative frequency is a measure of the number of times an event occurs in a sample, expressed as a proportion of the total number of events. To find the number of hot lunches sold on Friday, we multiply the total number of hot lunches sold in the week by the relative frequency of Friday. This gives us the number of hot lunches sold on Friday, which is 296 in this case. Understanding relative frequency is important in statistics as it helps to summarize data and understand the distribution of events.

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Answer:

360

Step-by-step explanation:

The formula for volume is length times width times height

so our equations is 3*12*10=360

The answers are given in the solution below.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is topics related to circle and its part we need to answer the question asked,

1) to 7) Given is a circle T,

a) Radius = TS, QT and RT all are the radius

b) Diameter = QS

c) Chord = PS

d) Central angle = ∠ RTQ

e) Minor arc = arc QR

f) Major arc = arc QSR

g) Semicircle = QPS

8) to 9) :-

a) Circle with radius 18 in :-

Circumference = 2π×radius = 2×3.14×18 = 113.04 in

Area = π·radius² = 3.14×18² = 1017.36 in²

b) Circle with diameter 25 m :-

Circumference = 2π×radius = 2×3.14×12.5 = 78.5 m

Area = π·radius² = 3.14×12.5² = 490.625 m²

10) The circle is having an area of 201.06 cm², we need to find the circumference and diameter,

Area = π·radius² = 201.06 cm²

radius² = 201.06 / 3.14

= 64

radius = 8 cm

Diameter = 16 cm

Circumference = 2π×radius = 2×3.14×8 = 50.24 cm

11) :-

Circle with radius P :-

The rule we will use here is :- arcs equal to central angle opposite to it, and full circle measures 360°

a) ∠ KPL = 90°

So, by linear pair sum, ∠ NPL = 90°

Now, by angle substitution law, ∠ NPM + ∠ MPL = 90°

∠ NPM = 27°

By using vertical angles rule, ∠ JPK = ∠ NPM = 27°

Therefore, arc JK = 27°

b) arc NJ = 180° - 27° = 153°

c) arc JL = 90°+27° = 117°

d) arc KNM = 360°-(90°+63°) = 207°

e) arc MJL = 360°-63° = 297°

f) arc JLK = 360°-27° = 333°

12) :-

arc CD + arc AD = 180°

Therefore,

19x-49°+5x+37° = 180°

24x-12 = 180°

24x = 192°

x = 8

Therefore,

arc CD = 5x+37 = 74°

13) :-

Length of an arc = central angle / 360° × 2π×radius

= 232° / 360° × 2 × 3.14 × 5 = 20.23 mm

14) :-

= 73° / 360° × 2 × 3.14 × 14.5 = 18.46 ft

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Summary statistics, especially the mean and covariance of the two variables, can be used to find the regression equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

In simple linear regression with one independent variable (x) and one dependent variable (y), the regression equation can be expressed as:

y = β0 + β1x

where β0 and β1 are the regression coefficients. The coefficients can be estimated using the following formulas:

β1 = covariance(x, y) / variance(x)

β0 = mean(y) - β1 * mean(x)

Here, covariance(x, y) is the covariance between the two variables, variance(x) is the variance of the independent variable x, mean(x) and mean(y) are the means of x and y, respectively.

These formulas assume that the data has been standardized (mean = 0, variance = 1) for convenience, but the results can be easily transformed back to the original scale by using the actual mean and variance of the data.

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Answer: 6x=37

Step-by-step explanation: Because it is.

The x intercept of f-1(x) is the y intercept of f(x). The y intercept of f-1(x) is the x intercept of f(x). A horizontal asymptote for f(x) produces a vertical asymptote for f-1(x). A vertical asymptote for f(x) produces a horizontal asymptote for f-1(x).

(2 1/2, 0)

f(x) = 2 1/2 - 3 1/3 * x

or

f(x) = 5/2 - (10/3)*x

f^-1(x) is the inverse of f(x), which is obtained replacing f(x) by x, and x by y, and solving for y, as follows:

x = 5/2 - (10/3)*y

(10/3)*y = 5/2 - x

y = (5/2)*(3/10) - x*(3/10)

y = (3/4) - (3/10)*x

f^-1(x) = (3/4) - (3/10)*x

at x-intercept, f^-1(x) = 0,

(3/4) - (3/10)*x = 0

(3/4) = (3/10)*x

x = (3/4)*(10/3)

x = 5/2 or 2 1/2

Largest even integer which cannot be written as the sum of two odd composite numbers is 38 if it is divisible by at least one positive integer other than 1 and itself.

The positive even integers which cannot be expressed as the sum of 2 composite odd numbers are: 2,4,6,8,10,12,14,16,20,22,26,28,32,38. This sequence is A118081.

All we have to do now is check the even numbers smaller than  44

. The largest,  42 is a multiple of  3 so it’s handled as  42=9+33 and the next one down,  40 is handled as  40=25+15.But the next one down is our culprit:  38 is not the sum of two odd composite numbers, as you can readily check.

First, what are these “odd composite numbers” anyway? The number  1is considered neither prime nor composite (it’s a unit), so it’s out.  3,5 and  7 are prime. The smallest odd composite number is, therefore,  9 and the next one is  15 .So we have  18=9+9 24=9+1 and  30=15+15 as some even numbers which can be written as a sum of two odd composites, but so far it doesn’t look promising: plenty of even numbers, like  10 or  20 or  32 cannot be so written.

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She sold $8,811 worth of cleaning contracts in total, rounded to the nearest dollar.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, Linda receives a 14% commission for every office that signs a contract for the cleaning services.

Here, we are interested in calculating the value of the cleaning contracts sold.

Let the total value of the cleaning contracts sold to be $x

Mathematically;

14% of x = 1233.60

14/100 * x = 1233.60

14x = 100 * 1233.60

x = 123360/14

x= 8,811.43

Therefore,  the total value of the cleaning contracts she sold, rounded to the nearest dollar will be $8,811.

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The inverses of the functions f(x) = x + 3 and f(x) = 2x + 4 are

y = x - 3 and x = (y + 4)/2.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

The first graph y = x + 3.

To find the inverse we'll solve for 'x'.

y = x + 3.

x = y - 3.

y = x - 3.

f⁻¹(x) = x - 3.

And,

y = 2x - 4.

2x = y + 4.

x = (y + 4)/2.

f⁻¹(x) = (x + 4)/2.

The graph of the function y = x + 3 is shifted 3 units up to y = x.

And the graph y = 2x - 4 is shifted 4 units down and is steeper than y = x.

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So, value of when y is 51, x is -17.

When y varies directly as x, the relationship between y and x can be expressed as y = kx, where k is the constant of proportionality. In this case, we know that y = 27 when x = -9, so we can use this information to find k:

27 = k * -9

27/-9 = k

-3 = k

Now that we have found the value of k, we can use it to find x when y is 51:

y = kx

51 = -3x

x = 51/-3

x = -17

So, when y is 51, x is -17.

A linear equation is an equation that represents a straight line when plotted on a graph. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the point at which the line intersects the y-axis. Linear equations can be used to model real-world situations that exhibit a constant rate of change, such as the relationship between time and distance traveled, or the cost of a product and the number sold.

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Answer:

The midpoint of AB is (-0.5, 0)

Step-by-step explanation:

( X1 plus X2 = -1/2 = -0.5, Y1 plus Y2 = 0

The area of this region is equal to [tex]\pi \cdot (\sqrt{35})^2 = 35\pi[/tex]

The equation for the set of complex numbers z such that the real part of 1/z is equal to 1/6 is given by:

Re(1/z) = 1/6

Since 1/z = 1/x + i/y,

Where x and y are the real and imaginary parts of z, respectively,

we can write the equation as:

(1/x)=(1/6) and [tex]$\frac{y}{x^2 + y^2} = \frac{1}{6}$[/tex]

From the first equation,

we have x = 6.

Substituting this value into the second equation, we get:

[tex]$\frac{y}{36 + y^2} = \frac{1}{6}$[/tex]

Solving for y,

we find that [tex]$y = \pm \sqrt{35}$[/tex].

So, the set of complex numbers z that satisfies the equation forms a circle centred at 6 + 0i with radius [tex]$\sqrt{35}$[/tex].

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No a subspace of a finite dimensional vector space cannot be an infinite dimensional vector space

This is due to the fact that a subspace is a subset of a larger vector space and must have the same dimension as its parent vector space. In other words we can say that, if the parent vector space is finite dimensions,then the subspace must be as well.

To put it in another way, a vector space is finite dimensional if it can be traversed by a limited number of vectors. A subspace can only be spanned by a subset of the vectors that span the parent vector space since it is a subset of a larger vector space. As a result, if the parent vector space has finite dimensions, the subspace must be as well.

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The probability that each player receives an ace is: 0.1055

let us consider they are  52 open spots in a row. We should divide the cards by placing them on these spots. This is the understanding that the cards on spots  1,2,…, and 13 are for a player, and the cards on spots  14,15,…, and 26 are for another player.

Then there are  134 ways to place the aces in such a way that each player will get an ace. This is the understanding that we do not discern suits. Next to that, there are 524 ways in total to place the aces.

So the probability that each player receives an ace is:

134(524)=28561270725=219720825≈0.1055

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The plots provides the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression is image 3.

Regression is one of the methods for determining cause-and-effect relationships between variables and other variables. In simple regression analysis, the relationship between variables is linear, where changes in variable X will be followed by changes in variables permanently. Whereas in a nonlinear relationship, changes in X are not followed by changes in variable Y proportionally.

The regression analysis method is used to produce a relationship between two or more variables in numerical form. The regression equation is the line equation that best represents the relationship between the two variables. Regression is divided into several types, namely simple regression, nonlinear regression, and multiple regression.

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a) Every Engineer loves to solve some problem.

x ∀ y(E(x) ∧ A(y) → ~L(x, y))

b) There is a smallest positive integer.

∀ x   y(N(x) ∧ M(y) → x < y)

c) All obtuse triangles have one angle that measures larger than 90°.

x(A(x)  → ~B(x) ∨ ~E(x))

d) There is a student in the class who helps all classmates.

∀x ∀y(C(x) ∧ A(y, x) → ~B(x, y))

a) Every Engineer loves to solve some problem.

The statement using multiple quantifiers and variables.

Let E(x) = x is an engineer

A(x) = x is a problem.

L(x, y) = x loves to solve probability

The negation of the given statement in words.

Negation: There exists at least one engineer who does not love to solve any problem.

The negation using multiple quantifiers and variables.

x ∀ y(E(x) ∧ A(y) → ~L(x, y))

b) There is a smallest positive integer.

The statement using multiple quantifiers and variables.

Let M(x) = x is a negative integer.

x ∀ y(M(x)  ∧ M(y) → x ≥ y)

The negation of the given statement in words.

There exists no longer negative integer.

The negation using multiple quantifiers and variables.

∀ x   y(N(x) ∧ M(y) → x < y)

c) All obtuse triangles have one angle that measures larger than 90°.

The statement using multiple quantifiers and variables.

Let A(x) = x is healthy.

B(x) = x follow diet plan.

C(x) = x follows exercise plan.

∀ x (A(x) → B(X) ∧ C(x))

The negation of the given statement in words.

There exists at least one healthy man who does not follow either diet plan or exercise plan.

The negation using multiple quantifiers and variables.

x(A(x)  → ~B(x) ∨ ~E(x))

d) There is a student in the class who helps all classmates.

The statement using multiple quantifiers and variables.

Let A(y, x) = y is classmate of x.

B(x, y) = x helps y.

C(x) = x is a student in the class.

x ∀ y (C(x) ∧ A(y, x) → B(x, y))

The negation of the given statement in words.

There is no student in the class who helps all classmates.

The negation using multiple quantifiers and variables.

∀x ∀y(C(x) ∧ A(y, x) → ~B(x, y))

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The complete question is:

For each of the statements in a, b, c, and d do the following:

(i) Rewrite the statement using multiple quantifiers and variables.

(ii) Write the negation of the given statement in words.

(iii) Rewrite the negation using multiple quantifiers and variables.

a) Every Engineer loves to solve some problem.

b) There is a smallest positive integer.

c) All obtuse triangles have one angle that measures larger than 90°

d) There is a student in the class who helps all classmates.

We can see here that the answer on angles is seen in the attached image.

Angles are geometric shapes that are formed by two rays or lines that start from a common point, known as the vertex. Angles can be classified based on their measurement, or size, in degrees.

There are:

We see that in the attached image, we have been able to show that the given statements are true about angles.

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The volume of the triangular prism in cubic centimeters is 1, 632 cm³

The formula for calculating the volume of a triangular prism is expressed as;

V = L × W × H÷ 2

Such that the parameters are;

Now, substitute the values, we get;

Volume, V = 8 × 12 × 34/2

Multiply all the values

Volume, V = 3264/2

Divide the numerator by the denominator

Volume, V = 1, 632 cm³

Hence, the value is  1, 632 cm³

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Answer:

1 and 2: Vertical angles

5 and 6: Adjacent angles

Step-by-step explanation:

In the first image, the two angles are opposite from each other and formed by the intersection of two lines, making 1 and 2 vertical angles.

In the second image, the two angles are right next to each other making 5 and 6 adjacent angles.

Vertical angles: opposite angles formed by the intersection of two lines

Adjacent angles: two angles that share a common vertex and a common side, but do not overlap

The subject's heart rate is 100 beats per minute.

There are three main methods of calculating ECG rate. There is no specific best method, and preference varies between clinicians. However, certain methods may be better suited for rhythms such bradyarrhythmia's or tachyarrhythmias.

To calculate the heart rate from an ECG recorded on millimeter grid paper, you can use the following formula:

Heart rate (beats per minute) = (recording speed (mm/s) / distance between cycles (mm)) x 60 s/min

Using the given information, the calculation would be:

Heart rate (beats per minute) = (25 mm/s / 15 mm) x 60 s/min = 100 beats per minute

Therefore, the subject's heart rate is 100 beats per minute.

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To calculate the 97% confidence interval, we can use the following formula:

CI = (mean - (critical value) * (standard deviation / square root of sample size), mean + (critical value) * (standard deviation / square root of sample size))

Where critical value is the t-value that corresponds to 97% confidence level and degrees of freedom (df) equal to n-1.

Using a t-distribution table with df = 103, the critical value is 1.98.

Putting  in the numbers:

CI = (12.05 - (1.98) * (0.08 / sqrt(104)), 12.05 + (1.98) * (0.08 / sqrt(104)))

CI = (12.05 - (1.98) * (0.08 / 10.197), 12.05 + (1.98) * (0.08 / 10.197))

CI = (12.05 - 0.0177, 12.05 + 0.0177)

CI = (12.0323, 12.0677)

So the 97% confidence interval for the mean amount of soda in a can is (12.0323, 12.0677) ounces.

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Answer:

f(x) = [tex]\frac{1}{2}[/tex] x

Step-by-step explanation:

a linear function has the form

f(x) = ax + b

to find a and b substitute ordered pairs from the table into f(x)

using (0, 0 )

0 = a(0) + b

0 = b

then

f(x) = ax + 0

using (- 4, - 2 )

- 2 = a(- 4) = - 4a ( divide both sides by - 4 )

[tex]\frac{-2}{-4}[/tex] = a , that is

a = [tex]\frac{1}{2}[/tex]

Then

f(x) = [tex]\frac{1}{2}[/tex] x

or

f(x) = 0.5x

The inequality equation is 10x + 9y ≥ 180 and the y-intercept is y ≥ 20 and the x-intercept is x ≥ 18

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

10x + 9y ≥ 180   be equation (1)

On simplifying the equation , we get

To calculate the y-intercept , substitute the value of x = 0

when x = 0

9y ≥ 180

Divide by 9 on both sides of the equation , we get

y ≥ 20

To calculate the x-intercept , substitute the value of y = 0

when y = 0

10x ≥ 180

Divide by 10 on both sides of the equation , we get

x ≥ 18

Hence , the x and y intercepts are x ≥ 18 and y ≥ 20 respectively

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Answer:

Points R(4,1) S(7,3) T(6,4) after translation

R(4-3, 1) S(7-3, 3) T(6-3, 4)

R'(1, 1) S'(4, 3) T'(3, 4)

Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection

R''(1, -3) S''(4, -5) T''(3, -6)

Step-by-step explanation:

Answer:Step-by-step explanation:Points R(4,1) S(7,3) T(6,4) after translation R(4-3, 1) S(7-3, 3) T(6-3, 4) R'(1, 1) S'(4, 3) T'(3, 4) Points R'(1, 1) ...

Answer:By solving a system of equations, we will see that the function is continuous for all values of x

Step-by-step explanation: