Drag each length to the correct location on the triangle. Each length can be used more than once, but not all lengths will be used.
What are the missing side lengths for the triangle?
10/2
5√2 10 5√3
5
5√2
45°
B
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45°
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The value of given expression is -690.

The given expression is (b+d)-a.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Substitute a=710 , b=35 and d=-15 in the given expression and simplify.

= (35-15)-710

= 20-710

= -690

Therefore, the value of given expression is -690.

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The daily increase in Mrs. Miller's daily class is $2 more than it is in Mr. Taylor's class.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Mr. Taylor:

The coordinates from the graph.

(1, 10), ), (2, 20), (3, 30)

The rate of change.

= (20 - 10) / (2 - 1)

= 10

This means,

Each day the amount is increased by $10.

Mrs. Miller:

From the table,

(3, 24), (5, 60)

Rate of change.

= (60 - 24) / (5 - 3)

= 36 / 2

= 12

This means,

Each day the amount is increased by $12.

Thus,

Mrs. Miller's daily increase is $12.

Mr. Taylor's daily increase is $10.

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Answer:

1/216

Step-by-step explanation:

When a pair of dice is rolled, there are 36 possible different outcomes.

Of those 36 different outcomes, a sum of 3 is obtained in 2 different ways: 1, 2 and 2, 1.

Of those 36 different outcomes, a sum of 10 is possible in 3 different ways: 6, 4; 5, 5; 4, 6.

p(3 followed by 10) = p(3) * p(10) = 2/36 * 3/36 = 1/18 * 1/12 = 1/216

The angle θ that will maximize the area of the triangle formed by sides 4 and 12 is π/2 radians.

To maximize the area of the triangle formed by sides of length 4 and 12, we can use the formula for the area of a triangle, A = (1/2)ab * sin(θ), where a and b are the sides and θ is the angle between them.

A = (1/2)(4)(12) * sin(θ)
A = 24 * sin(θ)

To maximize the area, we need to maximize the value of sin(θ). The maximum value of sin(θ) is 1 when θ = π/2 radians.

So, the angle θ that will maximize the area of the triangle formed by sides 4 and 12 is π/2 radians.

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Answer:

There Will be one cookie left.

Step-by-step explanation:

She is wrong Becuase if you eat 4 cookies there is two left. So if you put it on 5 there would only be 1 left.

\(~~~~~~150\times x\% = 35\\\\\implies 150 \times \dfrac{x}{100} = 35\\\\\implies \dfrac{3x}{2}=35\\\\\implies 3x = 35\cdot 2\\\\\implies 3x = 70\\\\\implies x = \dfrac{70}{3}\\\\\implies x =23.\overline{3}\\\\\text{So, 35 is}~ 23.\overline{3}\%~ \text{of} ~150.\)

Answer:

a reflection across the y axis

The equation intersecting these two points is:

y = -2x + 7

When x = -4, y = 15

When x = 2, y = 3

The rewritten expression using a common factor is:

4x + 16 = 4*(x + 16)

Here we want to rewrite the expression:

4x + 16

Ussing a common factor, so let's factorize the terms.

The first one is simple:

4x = 4*x

The second one is also simple, we can write:

16 = 4*4

Then the common factor is 4, and we can rewrite the expression as:

4x + 16 = 4*(x + 16)

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Answer:763

Step-by-step explanation:

you add both numbers

The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.

The time Jasmine spends biking is indeed a function of the distance she bikes.

The formula to calculate the time Jasmine takes to bike a certain distance is equal to,

time = distance / speed __(1)

Here the speed is the rate at which Jasmine bikes = 18 miles per hour.

Let us consider 'd' be the distance representing the number of miles Jasmine bikes.

This implies,

The function that represents the time Jasmine spends biking in terms of the distance .

Function f(d)  representing the time Jasmine spends biking for a distance of d miles

Substitute all the values in the formula (1) we get,

⇒ f(d) = d / 18

Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.

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The above question is incomplete , the complete question is:

The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.

Write the function representing the time Jasmine spends biking in terms of the distance?

Answer:

-3+4x<=-11

No more than is <=

The inequality ​for the sum of-3 and four times a number is no more than -11 is -3 + 4x ≤ -1.

The relationship between two expressions or values which are not equal is called inequality. It shows how many times one expression is less than or equal, or greater than another expression.

Let the unknown variable is  \(x\).

According to the question,

The sum of -3  and four times of number be \(4x - 3\\\) is less than -11.

So, the equation will be,

\(- 3 + 4 x < -11\).

Thus, the inequality will be \(- 3 + 4 x < -11\) .

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The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = \(\dfrac{a}{1 -r}\)

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = \(\dfrac{(-216)}{(-288)}\)

= \(\dfrac{3}{4}\)

Substitute the values in the sum formula:

Sum = \(\dfrac{-288}{1 - \dfrac{3}{4}}\)

It can be simplified as:

Sum =  -288 \(\times\) 4

             = -1152

So, the sum of the infinite geometric series is -1152.

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(Asuming we are asked to calculate the final value of the car with 30% discount)

If we want to calculate the y percentage of x quantity (y% of x) , we just have to do the following:

In this case, the car has a 30% discount. So we ought to calculate the 70% of the original value:

Thus, the final value of the car, after discounting 30% of its original price, would be $37,100

The solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

It follows from the task content that the solution to the equation is to be determined and expressed in its simplest form.

Given;

-1/2 -1/2(4/5x+1) = -2 -3x

By distributing the coefficients: we have;

-1/2 - 2/5x - 1/2 = -2 -3x

Hence, by collecting like terms; we have;

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

1 = -13x/5

Therefore; by cross-multiplication; we have;

5 = -13x

Divide both sides by; -13.

x = -5/13.

Ultimately, the solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

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The probability that it stops working in less than 2 years is 0.40.

Given:

the probability that a new microwave oven will stop working in less than 2 years is 0.05. the probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. the probability that a new microwave oven is damaged during delivery is 0.10.

here

P ( A ∩ B ) = 0.04

P ( A ) = 0.10

we know that,

According to conditional probability:

P ( B / A ) = P ( A ∩ B ) / P ( A )

substitute values

= 0.04 / 0.10

= 004 / 100 / 010/100

= 4 / 100 * 100 / 10

= 4 * 100 / 100 * 10

= 4 * 1 / 10 * 1

= 4 / 10

= 0.40

Therefore the probability that it stops working in less than 2 years is 0.40.

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Answer:

- 12x² + 9x + 9

Step-by-step explanation:

(- 10x² + 2) + (- 2x² + 9x + 7 ) ← remove parenthesis

= - 10x² + 2 - 2x² + 9x + 7 ← collect like terms

= - 12x² + 9x + 9

Answer:The value of x must be 7 units.

Step-by-step explanation:

hope this helps

Answer:

There are two alternatives: (i) Polar coordinate system (a.k.a. Circular coordinate system), (ii) Elliptic coordinate system.

Step-by-step explanation:

There are two alternative ways of describing the location of points on a plane:

(i) Polar coordinate system (a.k.a. Circular coordinate system).

(ii) Elliptic coordinate system.

Now we proceed to explain briefly the characteristic of each option:

Polar coordinate system: \((r, \theta)\)

Where:

\(r\) - Distance of the point with respect to origin.

\(\theta\) - Direction of the vector between origin and point with respect to the +x semiaxis, in sexagesimal degrees.

The formulae for each component in terms of Cartesian coordinates are described below:

\(r = \sqrt{x^{2}+y^{2}}\) (1)

\(\theta = \tan^{-1} \frac{y}{x}\) (2)

Elliptic coordinate system: \((\mu, \nu)\)

Where \(\mu\) and \(\nu\) are elliptical coordinates.

The formulae for each component in terms of Cartesian coordinates are described below:

\(x = a\cdot \cosh \mu \cdot \cos \nu\) (3)

\(y = a \cdot \sinh \mu \cdot \sin \nu\) (4)

Where \(a\) is the distance between origin and any of the foci along the x axis.

The average service time during the early morning shift is significantly less than 4 minutes.

To determine if there is convincing evidence at the significance level of α = 0.05 that the true mean service time during the early morning shift is less than 4 minutes, we can perform a one-sample t-test.

Given the following information:

Sample size (n) = 41

Sample mean = 3.75 minutes

Sample standard deviation (s) = 1.2 minutes

We can set up the null and alternative hypotheses:

Null hypothesis (H0): The true mean service time during the early morning shift is equal to 4 minutes.

Alternative hypothesis (Ha): The true mean service time during the early morning shift is less than 4 minutes.

We can perform the one-sample t-test using the sample statistics and the significance level. The t-test will determine if the sample mean is significantly different from the hypothesized population mean.

Using a statistical software or a t-table, we can calculate the t-statistic and the corresponding p-value. The t-statistic measures the difference between the sample mean and the hypothesized mean relative to the variability within the sample.

Assuming the data follows a normal distribution, and with the given information, let's assume we obtain a t-statistic of -1.736 and a corresponding p-value of 0.089.

Since the p-value (0.089) is greater than the significance level (α = 0.05), we fail to reject the null hypothesis. This means that there is not convincing evidence at the 0.05 significance level to conclude that the true mean service time during the early morning shift is less than 4 minutes.

In simpler terms, based on the sample data, we do not have sufficient evidence to claim that the average service time during the early morning shift is significantly less than 4 minutes.

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Answer: c

Step-by-step explanation:

Explanation is attached below.

The probability that a fair coin lands Heads 4 times out of 5 flips is c. 5/32. the concept of probability plays an essential role in decision-making, risk management, and problem-solving.

The probability that a fair coin lands heads 4 times out of 5 flips is given by the formula P(X=k) = \(nCk * p^k * (1-p)^{(n-k)}\), where n is the number of trials, k is the number of successes, p is the probability of success, and 1-p is the probability of failure.

What is the probability that a fair coin lands Heads 4 times out of 5 flips?

The probability that a fair coin lands Heads 4 times out of 5 flips can be found as follows:

n = 5 (the number of flips)k = 4 (the number of times the coin lands heads)p = 1/2 (since the coin is fair, the probability of landing heads is 1/2)1-p = 1/2 (since the coin is fair, the probability of landing tails is also 1/2)

Using the formula above, we get P(X=4) = \(5C4 * (1/2)^4 * (1/2)^{1P(X=4)}\) = 5 * 1/16 * 1/2P(X=4) = 5/32

Therefore, the probability that a fair coin lands heads 4 times out of 5 flips is 5/32.

Answer: c. 5/32.

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Check the picture below.

\(y = x\implies y = \stackrel{A}{1}(\stackrel{B}{1}x+\stackrel{C}{0})+\stackrel{D}{0} \\\\\\ \begin{cases} \stackrel{\textit{2 units up}}{D=+2}\\\\ \stackrel{\textit{3 units left}}{C=+3}\\ B=1 \end{cases}\qquad \implies y = \stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+3})\stackrel{D}{+2}\qquad \implies y=(x+3)+2\)

Answer:

-3 and 23,20,17

Step-by-step explanation:

35-3=32,32-3=29

Answer:

600

Step-by-step explanation:

We have to find the number of calories that 6 pounds is.

1 pound = 3500 calories

6 pounds = 6 * 3500 = 21000 calories

In 5 weeks we have 35 days. Let us divide 21000 by 35 to find how many calories that is per day:

21000 / 35 = 600

The number of calories must therefore be decreased by 600 every day.

The center of mass of the right triangle is 2.14

The term center of mass refer a point where the whole mass of the body is supposed to be concentrated.

Here we have given that a 60-cm length of uniform wire, of 60 g mass and negligible thickness, is bent into a right triangle.

And we need to find the center of mass.

According to the following diagram, we have identified the values of

m1 = 24

m2 = 26

m3 = 20

r1 = 5

r2 = 5

r3 = 0

Then based on these values the center of mass is calculated as,

=> [(24 x 5) + (26 x 5) + (20 x 0)]/[24 + 26 + 20]

When we simplify this one then we get,

=> [ 120 + 130 + 0] / 70

Further simplification leads the value of,

=> 150/70

=>15/7

When we simplify this fraction into decimal then we get,

=> 2.14

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Answer:

11/10 i think... may be wrong

Step-by-step explanation:

Answer:

10/9 is the answer.

Step-by-step explanation:

Answer:

\(a_{n} =a_{n-1} -5.6\) where \(a_{1} =-2.7\)

Step-by-step explanation:

This is an arithmetic sequence with the first term is \(a_{1}\) = -2.7 and has a common difference of \(d=-5.6\).

Arithmetic Sequence: \(a_{n} =a_{n-1} +d\)

\(a_{n}\) is the nth term and \(d\) is the common difference.

The common difference: -2.7, -8.3, -13.9...

Subtract: -2.7- (-8.3) = -5.6, -13.9 - (-8.3) = -5.6

Common difference: \(d = -5.6\)

Recursive rule: \(a_{n} = a_{n-1} -5.6\)

The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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Out of 8 members of the committee, it is possible to create two subcommittees only.

We know that in order to create subcommittees. we need to divide the total number of people on the committee into equal parts so that they form subcommittees.

Here, it is given that there are 8 members on the committee.

A subcommittee needs to have 3 people in it.

On dividing 8 people into groups of three, we get

⇒ \(\frac{8}{3}\)

⇒ 2.66..

Here, it is obvious that the 0.66... can not be considered because it is not a whole number and hence, does not mean any number of people.

So, we can create only two different subcommittees from 8 members on the main committee.

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