Given △RST≅△LMN, m∠R=65°, and m∠M=70°, what is the measure of ∠T?

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m∠T=

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

The number of tiles that would be grey tiles out of the total tiles given would be = 28 tiles.

To calculate the number of grey tiles, the total number of tiles given should be divided into two since the path is made up of only white and grey tiles.

The total number of tiles = 56 tiles.

Therefore the grey and the white tiles have the same number of tiles = 56/2 = 28 grey tiles

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Answer:

63

Step-by-step explanation:

b x h = A

9 x 7 = 63

The whole number for "forty-two thousand, fifteen" is 42,015.

We have, "forty-two thousand, fifteen".

To write a sentence as a whole number using digits, you would typically replace the words with their numerical representations. Here's an example:

Sentence: "I have three apples and four bananas."

Whole number: "I have 3 apples and 4 bananas."

Here the numeric terms are forty- thousand and fifteen then the numerical digit will be

= 42, 015.

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The correct statement is:

"Divide out a common factor of x - 7." The limit of the given expression is 1/6.

Multiply by (√(x + 2) + 3)/(√(x + 2) + 3):

This statement is not correct.

We generally multiply by the conjugate of the expression to eliminate square roots, but in this case, multiplying by (√(x + 2) + 3)/(√(x + 2) + 3) does not help simplify the expression.

Get x - 1 in the numerator:

This statement is not correct. The expression does not involve x - 1 in the numerator.

Get (x - 7)(√(x + 2) - 3) in the denominator:

This statement is not correct. We want to simplify the expression, not introduce a more complex denominator.

Divide out a common factor of x - 7:

This statement is correct. By factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.

Calculate the limit as 1/6:

This statement is not correct. We need to perform further simplification to determine the limit.

After canceling out the common factor of x - 7, the simplified expression becomes:

lim x -> 7 (√(x + 2) - 3)/(x - 7) = lim x -> 7 1/(√(x + 2) + 3)

To find the limit, we substitute the value x = 7 into the simplified expression:

lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6

Therefore, the correct statement is: "Divide out a common factor of x - 7." The limit of the given expression is 1/6.

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The maximum distance of the fire engine from the school is D = 4.5 miles

Given data ,

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the first point be P = P ( -4 , -3 )

Let the second point be Q = Q ( -7 , -3 )

First distance D₁ = √ ( -4 + 7 )² + ( -3 + 3 )

D₁ = √9

D₁ = 3 units

Now , each unit on the grid represents 1/2 mile

And , the distance from P to school is S ( -4 , 3 )

D₂ = √ ( -4 + 4 )² + ( -3 - 3 )²

D₂ = √36

D₂ = 6 units

So , the total distance D = 3 + 6 = 9 units

And , the distance in miles = 9/2 = 4.5 miles

Hence , the distance is 4.5 miles

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The complete question is attached below :

A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?

Answer:

  Option 3: y = 1/3x +67

Step-by-step explanation:

You want the equation of the best-fit line in slope-intercept form for the data given.

The attached calculator display shows the best-fit line for the data, where x is in minutes, is approximately ...

  y = 0.41x + 64

The closest answer choice is ...

  Option 3: y = 1/3x +67

__

Additional comment

The second attachment shows a plot of the data (study minutes, test score) with the best-fit line in red, and the Option 3 line in blue.

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The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.

Let's compare the intensities of the two earthquakes using the Richter scale.
Step 1: Understand that the Richter scale is logarithmic, which means each whole number increase represents a tenfold increase in intensity.
Step 2: Determine the difference between the magnitudes of the two earthquakes. The Gansu earthquake measured 8.6, and the earthquake causing no damage measured 4.
8.6 - 4 = 4.6
Step 3: Calculate the intensity ratio between the two earthquakes using the difference in magnitudes. Since each whole number increase represents a tenfold increase in intensity, we need to raise 10 to the power of the difference.
10^4.6 ≈ 39,810.71705535
Step 4: Round the result to a whole number.
39,810.71705535 ≈ 39,811
The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.

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Answer:

1 1/5 = 6/5

1 1/3 = 4/3

Step-by-step explanation:

hope this helps, if you’re looking for 1 1/5 + 1 1/3 please tell me and I will solve that for you

Answer:50

Step-by-step explanation:

Answer:

-------------------

As per definition, the cosine function is:

Since triangles are similar, the ratio of corresponding sides is same:

Answer:

She spends 70 minutes in total or 1h 10min

PLEASE MARK IT THE BRAINLIEST!!!!!

Answer:

La suma de los cuatro ángulos de un cuadrilátero es igual a 360 grados. Entonces, si dos ángulos miden 60° y 80°, la suma de esos ángulos es de 140 grados.

Los otros dos ángulos están en una proporción de 2:9, lo que significa que la suma de sus medidas es de 11 partes. Si representamos las medidas de estos ángulos como 2x y 9x, respectivamente, entonces podemos escribir la ecuación:

2x + 9x = 11 partes

11x = 11 partes

x = 1 parte

Por lo tanto, el ángulo más pequeño mide 2x = 2 partes o 2 × 1 = 2 grados, y el ángulo más grande mide 9x = 9 partes o 9 × 1 = 9 grados.

En resumen, los dos ángulos faltantes miden 2° y 9°.

Step-by-step explanation:

The derivative of the function is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = log₂ ( 3x + 4 )³

On simplifying , we get

On taking the derivative of the function , we get

f' ( x ) = d/dx ( log₂ ( 3x + 4 )³ )

d/dx ( log₂ ( 3x + 4 )³ ) = 1/ ln ( 2 ) [ d/dx( 3x + 4 )³ ]

On applying chain rule , we get

f' ( x ) = 1/ ln ( 2 ) 1/( 3x + 4 )³ ( 9 ( 3x + 4 )² )

So , cancelling out the similar terms , we get

f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )

Hence , the derivative is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )

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Answer:

24.6%

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

n = 9, r = 4, p = 0.5

P = ₉C₄ (0.5)⁴ (1−0.5)⁹⁻⁴

P = 126 (0.5)⁴ (0.5)⁵

P ≈ 0.246

The type of test used in this problem is given as follows:

1 proportion z test.

At the null hypothesis, we consider if there is not enough evidence to conclude that the mean is different of 0.55, hence:

[tex]H_0: p = 0.55[/tex]

At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is different of 0.55, hence:

[tex]H_a: p \neq 0.55[/tex]

We are testing a proportion, hence the z-distribution is used, thus the correct option is given as follows:

1 proportion z test.

(in the case of a proportion, a z test is used, for sample means that we can use either z test or t test depending on the problem).

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Answer: To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the initial principal (the amount borrowed)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

In this case, we have:

P = $21,000

r = 8.75% = 0.0875

n = 1 (interest is compounded annually)

t = 13 years

So, plugging these values into the formula, we get:

A = 21,000(1 + 0.0875/1)^(1*13)

A = 21,000(1.0875)^13

A = $58,150.51

Therefore, if the loan is paid in full at the end of the 13-year period, $58,150.51 must be paid back, which includes the original principal plus the interest accrued over the 13-year period.

Step-by-step explanation:

the volume of a prism is

length × width × height

so, for the small prism we have

5 × 4 × height = 100 in

height = 100/20 = 5 i

for the large prism we have

5 × 4 × height = 200 in³

height = 200/20 = 10 in

the larger prism is 10/5=2 times taller than the small prism.

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Answer:90

Step-by-step explanation:

Answer:

0.66

Step-by-step explanation:

please read attachments

Answer:

slope = [tex]\frac{5}{9}[/tex] , y- intercept = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

5x - 9y = 45 ( subtract 5x from both sides )

- 9y = - 5x + 45 ( divide through by - 9 )

y = [tex]\frac{-5}{-9}[/tex] x + [tex]\frac{45}{-9}[/tex] , that is

y = [tex]\frac{5}{9}[/tex] x - 5 ← in slope- intercept form

with slope m = [tex]\frac{5}{9}[/tex] and y- intercept c = - 5

The correct variables which are continuous are,

1. Length of a frog's jump.

2. Monthly TV cable bills.

3. Lottery revenues of states.

4. Number of wheels of a car.

We have to given that;

To find correct variables which are continuous.

Since, The number of wheels of a car is a discrete variable, because it can only take certain integer values (2, 3, 4, etc.), while the other variables can take any real value within a certain range.

Hence, The correct variables which are continuous are,

1. Length of a frog's jump.

2. Monthly TV cable bills.

3. Lottery revenues of states.

4. Number of wheels of a car.

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Since the average rates of change of f and g cannot be determined from the given information provided.

We can find the average rate of change of function f over the interval [-6, -3) as:

The average rate of change of f;

= (f (6) - f (3)) / (6 - 3)

= (71 - 59) / 2 = 6

We have the two given points to set up equations:

-53 = a(3)^b - 41

-53 = a(5)^b - 41

0 = a(3^b - 5^b)

Since 3^b ≠ 5^b, we must have a = 0, that means g is not a valid exponential function passing through the given points.

Therefore,

We can conclude, that the average rates of change of f and g cannot be determined.

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if y varies inversely as the same of x, and y=7/4 when x = 1 then value of y is 7/12 when x=3

If y varies inversely as the same of x, we can write the equation:

y = k / x

where k is the constant of proportionality.

Let us find the value of constant of proportionality k:

y = 7/4 when x = 1

7/4 = k / 1

Apply cross multiplication we get:

7/4 = k

k=7/4

Now plug in the value of k to find y when x = 3:

y = k /x

y = (7/4) / 3

When a fraction is divided by the whole number then fraction is multiplied with reciprocal of the whole number.

y=7/4×1/3

Multiply the numerators and denominators.

y=7×1/4×3

We know that 7×1  is 7 and 4×3 is 12.

y=7/12

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The amount that the jeweler would charge Mrs. Luisa, given the prices of the successive jewelry would be $ 19, 680

The charge for repairing the jewelry pieces is calculated in a geometric progression:

= 6, 63, 63 ², 63 ³, ..., 63 ⁷

The sum of the first n terms in such a progression is:

S = a x (r ⁿ - 1) / ( r - 1 )

Seeing as there are 8 pieces of jewelry, the total cost to Mrs. Luisa would be:

S = 6 x ( 3 ⁸  - 1) / ( 3 - 1 )

S = 6 x ( 6561 - 1 ) / 2

S = 6 x 6560 / 2

S = 3 x 6560

S = $ 19, 680

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