1. Find the LCM of 35,14 using prime factorization.

2. Find the LCM of 15,12 using prime factorization.

3. Find the LCM of 5,9,15 using prime factorization.

4. Find the LCM of 8,10,12 Using Prime factorization.


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The proof that ΔRST is congruent to ΔQUT is given below.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

1. It is given that ΔQRT is equilateral. So all the sides and angles are of equal measure.

2. Given ∠TQU ≅ ∠SRT

3. Given sides QU ≅ RS

4. Then since sides QT and RT are side of equilateral triangle ΔQRT, they are equal .

So sides QT ≅ RT

5. So we have, two sides and included angle of ΔRST is equal to corresponding two sides and included angle of ΔQUT.

By SAS Congruence Theorem, both the triangles ΔRST and ΔQUT are congruent to each other.

Hence completed the proof using SAS Congruence theorem.

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Answer:

the second option is a function

Step-by-step explanation:

Hope this helps!      :3

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There are different ways to approach this question, but one possible method is to conduct a one-sample t-test using the formula t = (M - μ) / (s / sqrt(n)), where M is the sample mean, μ is the population mean (null hypothesis), s is the sample standard deviation, and n is the sample size. With the given information, the t-value is (1.6 - 0) / (0.8 / sqrt(16)) = 8.

The degrees of freedom is n - 1 = 15. Using a t-table or a calculator, the p-value for a one-tailed test with 15 degrees of freedom and a t-value of 8 is much smaller than .05 (e.g., < .0005). Therefore, we can reject the null hypothesis and conclude that women find a sense of humor to be important in a long-term relationship at a .05 level of significance. The correct answer is b.

Test 2 is associated with smaller critical values. The critical values for a t-test depend on the level of significance, the degrees of freedom, and whether the test is one-tailed or two-tailed. In general, a smaller level of significance or a larger sample size leads to smaller critical values (i.e., it becomes easier to reject the null hypothesis). Since Test 2 has a larger sample size than Test 1, it is more likely to detect a significant effect (i.e., have a smaller Type II error rate), and therefore requires smaller critical values to achieve a .05 level of significance. The correct answer is b.

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Matrix-vector multiplication is a linear operation because it satisfies the properties of scalar multiplication and vector addition, which are a(u+v) = au + av and a(cu) = cau, where a is a scalar and u and v are vectors.

Matrix-vector multiplication is a fundamental operation in linear algebra, where a matrix is multiplied by a vector to produce another vector. This operation is considered linear because it adheres to certain properties.

The first property is scalar multiplication, which states that multiplying a vector u by a scalar a and adding it to another vector v (a(u+v)) is equivalent to multiplying u by a (au) and v by a (av) separately and then adding the results (au + av). In other words, the operation distributes over vector addition.

The second property is the distributive property of scalar multiplication, which states that multiplying a vector u by a scalar c and then multiplying the resulting vector (cu) by another scalar a is equivalent to multiplying u by the product of the two scalars (cau). This property allows the scalar multiplication to be distributed over scalar multiplication.

These properties ensure that matrix-vector multiplication preserves the linearity of the underlying vector space. They enable the manipulation and analysis of systems of linear equations, transformations, and other mathematical operations involving matrices and vectors.

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Answer:

I believe the answer will be 27/3

Answer:

a. 3x +51=180

x=43

b. 3(43)+51 =180 51 degrees; 129 degrees

Step-by-step explanation:

3x +51 =180

3x=180-51

3x=129

x=43

Answer:

30

Step-by-step explanation:

The total number of students in the class is equal to 30 students.

What do you mean by percentage ?

Percentage is the relative value indicating one hundredth part of any quantity.

The number of students who were absent on a particular day is 6 students.

The number of absent students is 20 % of total number of students in the class. We know that percent meant something out of 100. Here , 20 % will be equal to :

= \(\frac{20}{100}\)

Let's assume total number of students in class be x.

To find out the total number of students in the class we need to divide the percent of absent students by number of absent students , that is :

x = 6 ÷ \(\frac{20}{100}\)

We know that if the division symbol is converted to multiplication then , we need to inverse the second term which is left to the division symbol , that is :

x = 6 × \(\frac{100}{20}\)

x = 6 × 5

or

x = 30 students

Therefore , the total number of students in the class is equal to 30 students.

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The parameter estimate is statistically different from zero when the absolute value of the t-statistic is greater than the critical value associated with the desired level of significance.

In hypothesis testing, the t-statistic is calculated by dividing the parameter estimate by its standard error. The t-statistic measures the number of standard errors the parameter estimate is away from the null hypothesis value (usually zero).

If the absolute value of the t-statistic is greater than the critical value, it means that the parameter estimate is significantly different from zero at the chosen level of significance. In other words, there is evidence to reject the null hypothesis and conclude that the parameter is not equal to zero.

The specific critical value depends on the desired level of significance and the degrees of freedom associated with the t-distribution. If the absolute value of the calculated t-statistic exceeds the critical value, it indicates that the parameter estimate is statistically significant and significantly different from zero.

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By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

It is given that  the total weight of your backpack and its contents is 13 3/8 pounds.

Also given , we want to carry no more than 15 pounds.

Let the number of bottles we can carry be x.

Each bottles weigh 3/4 pounds.

Total weight of the bottles = 3x/4 pounds.

Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .

Thus the statement equation formed is -

⇒ 107/8 + 3x/4 = 15

⇒ 3x/4 = 13/8

⇒ x = 13/6 = 2.166

∴  x ≈ 2

Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

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It can be noted that the volume of the ball which is a sphere will be 5572.45 cm³.

From the information given, the soccer ball has a radius of 11 cm. This will be calculated by using the volume of a sphere.

Volume = 4/3πr³

= 4/3 × 3.14 × 11³

= 5572.45 cm³

In conclusion, the correct option is 5572.45 cm³.

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The average depth of the water between krakatau and jakarta is 0.41 kilometers.

We have a function as ,

s= 356√d

where,

s = speed

d = depth of the water

If we have speed of tsunami as 60 kilometers per hour putting the value in the equation,

s= 356√d

60 = 356 √d

√d = 60/356

d = 0.41

Therefore, depth of the water between krakatau and jakarta is 0.41 kilometers.

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complete question:

A volcano erupted on the island of Krakatau, Indonesia. The eruption caused a tsunami(a type of wave) to form and travel into the Indian Ocean and into the Java Sea. The speeds(in kilometers per hour) that a tsunami travels can be modeled by s= 356√d where dis the depth (in kilometers) of the water.1.A tsunami from Krakatau hit Jakarta traveling about 60 kilometers per hour. What is the average depth of the water between Krakatau and Jakarta.

Answer:

f(7)=-4

Step-by-step explanation:

f(7)=10-2(7)

f(7)=-4

Answer:

-4

Step-by-step explanation:

f(7)=10-2(7)

f(7)= 10-14

f(7)= -4

Answer:

Step-by-step explanation:

__________________________________________________________

According to Calculator Soup,

Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal. The shortcut way to convert from a percentage to a decimal is by removing the percent sign and moving the decimal point 2 places to the left. Express 50% as a decimal. "Percent" means "per 100" or "over 100".

__________________________________________________________

The answers are Divide by 100 and Move the decimal point two places to the left.

__________________________________________________________

Hope this helps! <3

__________________________________________________________

Answer:

Step-by-step explanation:

Slope intercept form: y =mx +c

5x - 2y = 10

    -2y =  -5x + 10

\(\dfrac{-2y}{-2}=\dfrac{-5x}{-2}+\dfrac{10}{-2}\\\\\\y=\dfrac{5}{2}x-5\)

Answer: 6 gallons

Step-by-step explanation:

4/30  * 45  = 6

Answer:

jroteejktrsafh‍❤️♥️❣️❣️♥️♥️‍‍‍‍‍‍‍‍☘️

Answer:

1.5

Step-by-step explanation:

\(\frac{2x3}{4}= \frac{6}{4}\)  

\(\frac{6}{4}\)   ÷2=

\(\frac{3}{2}\)

Hope this helps     :)

Answer:

1 1/2 or 3/2

Step-by-step explanation:

2 x 3/4

6/4

3/2

1 1/2

Answer:

1/2 × |AB| × |OE|

Step-by-step explanation:

use the formula for finding the area of a triangle.

Answer:

1

Step-by-step explanation:

Answer:

The answer to your question is -½

Step-by-step explanation:

Correct me if I'm wrong. Have a good day :)

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 4700\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &11 \end{cases} \\\\\\ 4700=Pe^{0.04\cdot 11} \implies 4700=Pe^{0.44}\implies \cfrac{4700}{e^{0.44}}=P\implies 3027\approx P\)

I will set it up for you only.

Let a = adult tickets

Let s = student tickets

Here is your system of equations:

a + s = 800

12a + 8s = 7500

Answer: 227

Step-by-step explanation:

To find the 46th term of the sequence, we need to first determine the pattern of the sequence. We can see that the sequence increases by 5 between each consecutive term. Therefore, the common difference of the sequence is 5.

Using this information, we can find the \(n\)th term of the sequence using the formula:

\(\Large \boxed{an = a1 + d(n-1)}\)

where

Using the given terms, we have:

To find the 46th term, we substitute \(n = 46\) into the formula:

Therefore, the 46th term of the sequence is 227.

________________________________________________________

To find the pattern in the sequence, we can observe that each term is obtained by adding 5 to the previous term. Therefore, we can write the recursive formula for the sequence as:

\(\large a_1 = 2\)

\(\large a_n = a_{n-1} + 5\)

To find the 46th term, we can use the recursive formula to generate each term until we reach the desired term:

\(\large a_1 = 2\)

\(\large a_2 = a_1 + 5 = 2 + 5 = 7\)

\(\large a_3 = a_2 + 5 = 7 + 5 = 12\)

\(\large a_4 = a_3 + 5 = 12 + 5 = 17\)

\(\vdots\)

\(\large a_{46} = a_{45} + 5 \approx \boxed{227}\)

\(\therefore\) The 46th term of the sequence is approximately 227.

We can also write the explicit formula for the sequence as:

\(\large a_n = 5n - 3\)

To verify that this formula generates the same sequence as the recursive formula, we can substitute the value of n = 1, 2, 3, etc. and compare the results.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

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The solution to the given separable differential equation for u, with the initial condition u(0) = 7.

To solve the separable differential equation for u, we start by rearranging the equation f as:

(1/u) du/dt = e^(3u)/u + 10t/u

We can now integrate both sides of the equation with respect to t and u, separately. Starting with the left-hand side, we have:

∫(1/u) du = ln|u| + C1

where C1 is the constant of integration. For the right-hand side, we can use u-substitution by letting v = 3u, dv/du = 3, and du/dv = 1/3u. Substituting these values into the equation f and simplifying, we have:

(1/3) ∫e^v dv = (1/3) e^v + C2

where C2 is another constant of integration. Substituting v = 3u back into the equation and combining the constants of integration, we get:

ln|u| = e^(3u)/3 + 10t/3 + C

where C = C1 + C2. To solve for u, we exponentiate both sides of the equation:

|u| = e^(e^(3u)/3 + 10t/3 + C)

We can drop the absolute value since u(0) = 7 > 0, and simplify the exponential expression by using the properties of exponents:

u = e^(e^(3u)/3) * e^(10t/3 + C)

Finally, we use the initial condition u(0) = 7 to solve for C:

7 = e^(e^(3(7))/3) * e^(10(0)/3 + C)
7 = e^(e^21/3) * e^C
ln(7/e^(e^21/3)) = C

Substituting this value of C back into the equation for u, we get:

u = e^(e^(3u)/3) * e^(10t/3 + ln(7/e^(e^21/3)))

This is the solution to the given separable differential equation for u, with the initial condition u(0) = 7.

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