Find the length of the third side. If necessary, round to the nearest tenth.
10
6

Answer:

C. x= 4

Step-by-step explanation:

|x + 3| = 7

x + 3 = 7

x = 7 - 3

x = 4

Answer:

x = 4

Step-by-step explanation:

|x + 3| = 7

=> x + 3 = 7

=> x = 7 - 3

=> x = 4

Notice that the length AB is 12cm, the length AC is 14cm and BC equals 10cm.

By comparing those sides with AD=6cm, AE=7cm and DE=5cm respectively, we can see that:

Therefore, the scale factor is 2.

Answer:

593.76

Step-by-step explanation:

Round, 1 is smaller that 5, stays the same.

Answer:

600

Step-by-step explanation:

5 is the digit in the hundred place

Look at the number on the right. Since 9 is bigger than 5, you are going to round up. So you have 600

According one-way ANOVA, the test is false.

In the given question,

When comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment, a​ one-way ANOVA is appropriate. It is also appropriate in this​ situation, however, to compare two means at a time using multiple independent two sample​ t-tests. We have to check whether this is true or​ false.

We firstly learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the means of two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given method it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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Answer: (2, 18)

Step-by-step explanation:

When x=2, \(f(2)=2(3)^{2}=18\).

So, it should pass through (2, 18).

Answer:

0.56

Step-by-step explanation:

edu 2022

Based on the provided options, the expression that will complete step 3 in the proof is "2sin(x)cos(x)."

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The 95% confidence interval for the mean internet speed is approximately (34.986 Mbps, 37.414 Mbps).

To determine if the claim is supported by the data, we can perform a hypothesis test. We'll set up the following hypotheses:

Null hypothesis (H0): The mean speed of the internet connection is 35 Mbps.

Alternative hypothesis (H1): The mean speed of the internet connection is greater than 35 Mbps.

Since we have a sample mean and standard deviation, we can use a one-sample t-test. Assuming a significance level (α) of 0.05, we can calculate the t-value and compare it to the critical value from the t-distribution.

The t-value can be calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / √(sample size))

t = (36.2 - 35) / (4.32 / √(30))

t ≈ 1.653

For a one-tailed test at a 95% confidence level, the critical value (t-critical) with (n-1) degrees of freedom is approximately 1.699. Since the calculated t-value is less than the critical value, we fail to reject the null hypothesis. Therefore, the data does not provide sufficient evidence to support the claim that the mean speed of your internet connection is more than 35 Mbps.

What is the margin of error for the estimate of the mean internet speed?

The margin of error can be calculated using the formula:

Margin of Error = t-critical ×(sample standard deviation / √(sample size))

Using the t-critical value from the previous question (1.699) and the sample standard deviation (4.32) and sample size (30) provided in the information:

Margin of Error = 1.699× (4.32 / √(30))

Margin of Error ≈ 1.214 Mbps

Therefore, the margin of error for the estimate of the mean internet speed is approximately 1.214 Mbps.

What is the 95% confidence interval for the mean internet speed?

To calculate the confidence interval, we use the formula:

Confidence Interval = sample mean ± (margin of error)

Using the sample mean (36.2) and the margin of error (1.214) calculated in the previous questions:

Confidence Interval = 36.2 ± 1.214

Confidence Interval ≈ (34.986, 37.414)

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So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

The value of x for the given logarithm equation  log(x^2 + 7) base 4 = 2​ is x = ± 3.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

It is known that \(log_{a}b\) = c can be written as \(a^{c}\) = b.

Given that, log(x^2 + 7) base 4 = 2​

Therefore, x² + 7 = 4²

x² + 7 = 16

x² = 16 - 7 = 9

x² = 9

x = ±3

Hence "The value of x for the given logarithm equation  log(x^2 + 7) base 4 = 2​ is x = ± 3".

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The values of x in both expression are x ≤ 4.375 and x < -1

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

8x + 21 ≤ 56

This gives

8x ≤ 35

Divide by 8

So, we have

x ≤ 4.375

Secondly, we have

56 < 7(7-x)

Divide by 7

8 < 7-x

This gives

x < 7 - 8

Evaluate

x < -1

Hence, the values of x that makes 56 < 7(7-x) are values less than -1

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After 2 years, the population would be 675 mice.similarly, you can calculate the population for any given value of t by substituting it into the equation.

the biologist is studying a group of 75 mice whose population triples each year. the population of mice, denoted by m(t), can be calculated using the equation m(t) = 75 * (3)ᵗ, where t represents time in years.

in this equation, the base of the exponential term, 3, represents the rate at which the population grows each year. as the population triples every year, the base is 3.

the exponent, t, represents the number of years that have passed since the initial population count of 75 mice.

to find the population at a specific time t, you substitute the desired value for t into the equation.

for example, if we want to calculate the population after 2 years (t = 2), we would have:

m(2) = 75 * (3)²m(2) = 75 * 9

m(2) = 675

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Therefore, (a) ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars, (b) ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour, (c) Approximately 559 cars in the garage at t = 10.

(a) To find the number of cars entering the parking garage over the interval 0 ≤ t ≤ 10, we need to integrate the rate of cars entering the garage with respect to time. ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars.
(b) To find ′′(5), we need to differentiate the rate of cars leaving the garage with respect to time twice. ′′(t) = -65cos(0.281) and ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour. This value represents the rate of change of the rate of cars leaving the garage at t = 5.
(c) To find the number of cars in the parking garage at time t = 10, we need to subtract the total number of cars leaving the garage from the total number of cars entering the garage from t = 0 to t = 10. This gives approximately 559 cars in the garage at t = 10.


Therefore, (a) ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars, (b) ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour, (c) Approximately 559 cars in the garage at t = 10.

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Answer:

Neil:

Sima:

Step-by-step explanation:

Neil:

Sima:

Answer:

The given statement is true. Reason: Area of a square = side × side Therefore, two squares that have the same area will have sides of the same lengths.

hop this helps

mark me brainliest

Step-by-step explanation:

Answer:

d represents distance

d = -16.8

Step-by-step explanation:

From the question, we are to find the vale of d from the expression

12+d = -4.8

Subtract 12 from both sides

12+d-12 = -4.8-12

d = -4.8-12

d = -16.8

Hence the value of d that makes two equation true is 16.8

d represents distance

d represents distance

d = -16.8

12+d = -4.8

12+d-12 = -4.8-12

d = -4.8-12

d = -16.8

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Answer:

B

Step-by-step explanation:

x+x+94 = 180 (sum of angle of triangle)

2x+94 = 180

2x = 180-94

2x = 86

x = 86÷2

Therefore x = 43

Answer:

Step-by-step explanation:

The measure of angle ∠WOV is 60 degrees and The measure of angle ∠YOZ is also 60 degrees.

What is an angle?

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

∠WOX = 30

It can be seen that the ∠XOY and ∠VOX are equal and 90 degrees.

The measure of angle ∠WOV will be

∠WOV + ∠WOX = 90

     ∠WOV + 30 = 90

             ∠WOV = 60

The measure of angle ∠YOZ will be

∠WOX + ∠XOY + ∠YOZ = 180   (Supplementary angle)

          30 + 90 + ∠YOZ = 180

                           ∠YOZ = 60

Step-by-step explanation:

120÷24

    0   24⟌120

    0   24⟌120   0  

    0   24⟌120   -0      1

    00  24⟌120   -0      12 

   0   24⟌120   -0      12 

    00  24⟌120   -0      12    - 0     12 

   00  24⟌120   -0      12    - 0     120

Summary:

(i) To find the value of α such that the vectors v1, v2, and v3 are linearly dependent, we can set up a system of equations and solve for α.(ii) The Basis Theorem states that any set of linearly independent

(i) To check if v1, v2, and v3 are linearly dependent, we can set up the following equation:

c1v1 + c2v2 + c3v3 = 0,

where c1, c2, and c3 are constants. Substituting the given values of v1, v2, and v3, we have:

c1(3,7,7) + c2(1,4,4) + c3(α,1,1) = 0.

Simplifying this equation, we get the following system of equations:

3c1 + c2 + αc3 = 0,

7c1 + 4c2 + c3 = 0,

7c1 + 4c2 + c3 = 0.

We can solve this system of equations to find the value of α that satisfies the condition.

(ii) The Basis Theorem states that any set of linearly independent vectors that span a vector space can be used as a basis for that vector space. By applying the Basis Theorem to the vectors v1, v2, and v3, we can check if they form a basis for ℝ3. If they do, we can find the coordinates of a given vector, such as (2,3,5), in terms of the basis using Gaussian Elimination.

To apply Gaussian Elimination, we set up the augmented matrix [v1 | v2 | v3 | b], where b is the given vector (2,3,5). Then we perform row operations to obtain the row-echelon form of the augmented matrix. The resulting matrix will allow us to determine the coordinates of b in terms of the basis vectors.

By performing the Gaussian Elimination process, we can find the coordinates of (2,3,5) in terms of the basis vectors.

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There is no value of α that makes the vectors linearly dependent, and the basis for ℝ³ using the vectors [377, 148, 11α] is {v₁, v₂, v₃}, with the coordinates of [2, 3, 5] in terms of the basis found through Gaussian Elimination.

(i) To find the value of α such that vectors v₁, v₂, and v₃ are linearly dependent, we need to determine if there exist scalars a, b, and c, not all zero, such that a(v₁) + b(v₂) + c(v₃) = 0. Substituting the given values, we have a(377) + b(148) + c(11α) = 0. By solving this equation, we can find the value of α that satisfies the condition for linear dependence.

(ii) The Basis Theorem states that any set of linearly independent vectors that spans a vector space forms a basis for that vector space. Using a different value of α than the one found in (i), we can apply the Basis Theorem to determine a basis for ℝ³ using the vectors v₁, v₂, and v₃.

By performing Gaussian Elimination or row reduction on the augmented matrix [v₁ v₂ v₃], we can determine the basis vectors. The coordinates of vector [2 3 5] in terms of the basis can be found by solving the system of equations formed by equating the linear combination of the basis vectors to [2 3 5].

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Answer:

Step-by-step explanation:

Converting 0.632 to a fraction, Step-by-Step

Step 1:

The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.

Step 2:

Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:

\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}

1×1000

0.632×1000

​

=

1000

632

​

Step 3:

Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:

\frac{632}{1000} = \frac{79}{125}

1000

632

​

=

125

79

​

Answer:

Rise and run

Step-by-step explanation:
Lets have it in slope intercept form
y=3/5x

Therefore our slope is 3/5 and y-intercept is (0,0)

Now we can start to graph. Start on our Y-intercept which is zero. Let's count 3 spaces up, which is our rise, then lets count 5 spaces to our right, which is our positive run, and plot a dot on our final point. You can do the same negative to graph our opposing points. Start on our 0,0 y-intercept, and count down 3 spaces. Then count 5 spaces to the left, and plot a dot on your final point. Now, let's draw a line through our points (-5, -3), (0,0), and (5,3)!

Answer:

The answer is d

Step-by-step explanation:

simplyfied into the simpiliest form possible

The simplest form of the equation is \(\rm10.7a-8.1b\).

We have to determine

What is the simplest form of the expression?

Expression; \(\rm (14.2a + 9.8b) - (13.1b -0.2a) - (3.7a + 4.8b)\)

To determine the simplest form of the equation following all the steps given below.

To subtract the expressions we multiply the negative sign inside the second parenthesis, change the sign of each term in the second and third parenthesis.

\(\rm = (14.2a + 9.8b) - (13.1b -0.2a) - (3.7a + 4.8b)\\\\= 14.2a+9.8b -13.1b+0.2a-3.7a-4.8b\\\\= 14.2a+0.2a-3.7a+9.8b -13.1b-4.8b\\\\= 10.7a-8.1b\)

Hence, the simplest form of the equation is \(\rm10.7a-8.1b\).

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The largest number of edges in the undirected graph with 'n' vertices which is before it present cycle is equal to n( n - 1 ) / 2.

Therefore, the largest possible number of edges in the undirected graph which has 'n' vertices  before it contain a cyclic is equal to n ( n - 1 ) / 2.

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Answer:

3:15 cause a mirror cant change time

Step-by-step explanation:

go in ur mirror and look at the time did it somehow get darker or lighter???

Answer:

8:45 i think

Step-by-step explanation:

5. The solution to the differential equation (ex + y)dx + (2 + x + yey)dy = 0 with y(0) = 1 is y = 2e^(-x) – x – 1. 6. The solution to the differential equation (x + y)²dx + (2xy + x² – 1)dy = 0 with y(1) = 1 is y = x – 1.

5. To solve the differential equation (ex + y)dx + (2 + x + yey)dy = 0 with the initial condition y(0) = 1, we can use the method of exact differential equations. By identifying the integrating factor as e^(∫dy/(2+yey)), we can rewrite the equation as an exact differential. Solving the resulting equation yields the solution y = 2e^(-x) – x – 1.
To solve the differential equation (x + y)²dx + (2xy + x² – 1)dy = 0 with the initial condition y(1) = 1, we can use the method of separable variables. Rearranging the equation and integrating both sides with respect to x and y, we obtain the solution y = x – 1.
These solutions satisfy their respective initial conditions and represent the family of curves that satisfy the given differential equations.

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