pls will heart and give 5 stars if you answer within 2-3 min

Answer:

117°

Step-by-step explanation:

Arc ABC (AB + BC) is intercepted by angle D.

Therefore, Arc ABC is 2 × m<D. (Inscribed Angle Theorem)

AB = 91°

m<D = 104°

Let BC = x

Arc ABC = (91° + x)

Thus,

91° + x = 2 × 104°

Solve for x

91 + x = 208

Subtract 91 from both sides

91 + x - 91 = 208 - 91

x = 117

Measure of arc BC = 117°

Answer:

y = -6x + 6

Step-by-step explanation:

y = mx + b

y = -6x + 6

The equation in slope-intercept form for the line with slope -6 and y-intercept 6 is y = -6x+6

The slope intercept formula y = mx + c is used when you know the slope of the line to be examined and the point given is also the y intercept (0, c).

Given that, a line has slope -6 and y-intercept 6.

The general form of the slope-intercept form for the line is y = mx+c, where m is the slope and c is the y-intercept.

Therefore, the required equation will be =

y = -6x+6

Hence, the equation in slope-intercept form for the line with slope -6 and y-intercept 6 is y = -6x+6

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Answer:

A: sf 2 or 1/2

Step-by-step explanation:

Answer:

Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4

Part B:

P''(-1, 0)

Q''(0, -1)

R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are not congruent.

Step-by-step explanation:

172 cm is approximately 5 feet and 7.72 inches.

To convert from cm to feet and inches, you can use the conversion factor 1 cm = 0.393701 inches. To convert 172 cm to inches, you would multiply 172 by 0.393701, which gives you 67.716566 inches.

Then, you can divide the total number of inches by 12 to get the number of feet, which in this case is 5.6430472 feet. Finally, you can subtract the number of feet from the total number of inches to get the remaining inches, which in this case is 7.716566 inches.

Therefore, 172 cm is equivalent to 5 feet and 7.72 inches.

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A linear function models the number of calories a 150-lb person burns from walking at a pace of 3 mph for x minutes  we can write the linear function:y = 3.76x - 0.4

In this scenario, Kevin weighs about 150 lb and walks at a pace of about 3 mph. When he walks for 15 min, he burns 56 Cal and when he walks for 60 min, he burns 225 Cal. From this information, we can write a linear function that models the number of calories a 150-lb person burns from walking at a pace of 3 mph for x minutes.

Linear function is an equation that represents a straight line on a graph. The general form of a linear function is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

The information given in the scenario that enables us to write a linear function is the rate at which Kevin burns calories while walking for different durations. Since Kevin burns 56 Cal in 15 min and 225 Cal in 60 min, we can use these two data points to find the slope of the line.

Slope (m) = (y₂ - y₁) / (x₂ - x₁)where (x₁, y₁) = (15, 56) and (x₂, y₂) = (60, 225)Slope (m) = (225 - 56) / (60 - 15)Slope (m) = 169 / 45Slope (m) = 3.76 (approximately)Therefore, the slope of the line that models the number of calories a 150-lb person burns from walking at a pace of 3 mph is 3.76.

Now we need to find the y-intercept (b). We can use any of the two data points to find the y-intercept. Let's use the first data point (15, 56).y = mx + by = 3.76x + b56 = 3.76(15) + bb = 56 - 56.4b = -0.4 (approximately)Therefore, the y-intercept of the line that models the number of calories a 150-lb person burns from walking at a pace of 3 mph is -0.4.

Now we can write the linear function:y = 3.76x - 0.4This function models the number of calories a 150-lb person burns from walking at a pace of 3 mph for x minutes.

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The general solution to the given differential equation using the method of variation of parameters is y(t) = c₁y₁(t) + c₂y₂(t), where y₁(t) = t∫(y₂(t)g(t)) / (W(t)) dt + c₁y₁(t) and y₂(t) = -t∫(y₁(t)g(t)) / (W(t)) dt + c₂y₂(t), and W(t) is the Wronskian of y₁(t) and y₂(t).

We are given a second-order linear differential equation of the form ty'' + (5t - 1)y - 5y = 41²est, where y₁(t) and y₂(t) are linearly independent solutions to the corresponding homogeneous equation. We can use the method of variation of parameters to find a general solution to the given equation.

By applying the variation of parameters method, we can express the general solution as y(t) = c₁y₁(t) + c₂y₂(t), where c₁ and c₂ are constants to be determined. However, the particular solutions y₁(t) and y₂(t) are not explicitly given, but we need to use them in the variation of parameters formulas.

To find the particular solutions y₁(t) and y₂(t), we use the formulas y₁(t) = -t∫(y₂(t)g(t)) / (W(t)) dt + c₁y₁(t) and y₂(t) = t∫(y₁(t)g(t)) / (W(t)) dt + c₂y₂(t), where g(t) = 41²est and W(t) is the Wronskian of y₁(t) and y₂(t). The Wronskian can be calculated as W(t) = y₁(t)y₂'(t) - y₁'(t)y₂(t).

By substituting the given functions and solving the integrals, we can find the particular solutions y₁(t) and y₂(t). Then, we combine them with the constants c₁ and c₂ to obtain the general solution y(t) = c₁y₁(t) + c₂y₂(t) to the given differential equation.

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then

Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).

Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.

The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.

In this case one rational zero is x=2.

This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)

That is:

2x³-5x²-19x+42/ x-2

= 2x² - x - 21, this means that

2x³-5x²-19x+42 =  (2x² - x - 21) * (x-2)

From the above, our constants are given as:

a = 2, b = -1 and c = 21

Multiply the constant terms by the leading coefficient.

a *x = -42

Find out two number that multiply to a*c = -42 and add b = -1

Next we identify all pairs of numbers with a product of -42. They are:

Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.

Next, replace the middle term -1x with 6x-7x to get:

(2x²  −x−21) * (x-2) =(2x²  +6x−7x−21) * (x-2)

If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).

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Full Question:

Factorise 2x³-5x²-19x+42

Using the basic percentage change rule, the answer is 6.5%.

In essence, percentages are fractions with a 100 as the denominator. In order to indicate that a number is a percentage, the percent symbol (%) is placed next to the number.

The required formula is:

\(Percentage = \frac {change}{inital} * 100\)

initial=72000

final=76680

change=76680-72000

=4680

% change = 4680 / 72000 * 100

=6.5%

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Answer:

=[7]+|-3| solve for the absolute value {-3 ->3}

=7+3

=10

Answer:

10

Step-by-step explanation:

Whenever you see those numbers in those specific brackets, it's asking for the absolute value of that number.

The absolute value is the distance from 0.

So, if you see -3 in those brackets, it's 3 because both -3 and 3 are 3 spaces from 0.

So 7 + 3 = 10.

Answer:

At most, 8 apples and apricots can be arranged at 4 plates, so that each plate contains 2 apples and 5 apricots.

Step-by-step explanation:

they are asking for the GREATEST amount of plates, but there are less apples than apricots so we must find the GCF, which is 4. then you divide the amount of apples by 4 as well as the amount of apricots by 4.

hope this helped :D

Answer: 25.33

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

\(\frac{x}{28}=\frac{38}{42}\\\\x={28} \left(\frac{38}{42} \right) \approx \boxed{25.33}\)

Answer:

Approximate population ≈ 74.36 million.  

Step-by-step explanation:

The given problem involves modeling of an exponential growth or decay function of a population.      

We can model the exponential growth of a population using the following Exponential Growth Model:

Where:

Based from the given equation, \(\displaystyle\mathsf{y\:=\:58.7(1.03)^t }\) , we can infer that:

⇒   \(\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }\) or  \(\displaystyle\mathsf{y\:=\:P_0 (1\:+\:r)^t }\)

Where:

Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :

\(\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }\)

⇒   \(\displaystyle\mathsf{P(8)\:=\:58.7 (1\:+\:.03)^8 }\)

Step 2: Follow the order of operations, addition inside the parenthesis:

⇒   \(\displaystyle\mathsf{P(8)\:=\:58.7 (1.03)^8 }\)

Step 3: Follow the order of operations, applying the exponent into the parenthesis (do not round off the digits inside the parenthesis):

⇒  \(\displaystyle\mathsf{P(8)\:=\:58.7 (1.266770081) }\)  

Step 4: Follow the order of operations, multiplying  58.7 (P₀) into the parenthesis:

⇒  \(\displaystyle\mathsf{P(8)\:\approx \:74.35940378\quad or \quad 74.36\:\:million}\)

Therefore, the approximate population of the country in January 2002 is 74.36 million.  

Exponential functions

Exponential growth

Exponential decay

Exponential growth model

____________________________

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The system of equations solved by the elimination method gives (-2, 1)

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

y = -4x + 11

y = 1/2x + 2

Subtract the equations to eliminate y

So, we have the following representation

-4 1/2x - 9 = 0

So, we have

-4 1/2x = 9

Divide the equations

x = -2

Recall that

y = 1/2x + 2

So, we have

y = 1/2(-2) + 2

This gives

y = 1

Hence, the solutions are x = 2 and y = 1

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Answer:

wHOLE number

Step-by-step explanation:

IT is a whole number

Answer:

2y+10/y

Step-by-step explanation:

Plato

Answer:

2(y+5)/y

Step-by-step explanation:

edmentum

Step-by-step explanation:

\(ĀB = (12 \times 2) \\ = 24\)

Answer:

4.12, 4.4, 4.6, 4.6 repeating. hope this helps!

The frequency of each range in the table is as follows:-

Range       Frequency

\(0-4\)                \(2\)

\(5-9\)                \(3\)

\(10-14\)             \(6\)

\(15-19\)             \(0\)

\(20-24\)             \(1\)

\(25-29\)             \(2\)

The frequency of a particular value is the number of times the value occurs in the data.

First, find the number of times the particular value occurs in the given data.

Given, Raphael surveyed his co-workers to find out their spent hours on the internet each week.

The results are:-

\(14,22,10,6,9,3,13,7,12,2,26,11,13,25\)

Thus, the number of occurence of a particular range can be written as follows:-

Range        Hours in given data       Frequeny

\(0-4\)                     \(3,2\)                              \(2\)

\(5-9\)                    \(6,9,7\)                            \(3\)

\(10-14\)           \(14,10,13,12,11,13\)             \(6\)

\(15-19\)                     \(0\)                               \(0\)

\(20-24\)                    \(22\)                              \(1\)

\(25-29\)                  \(26,25\)                           \(2\)

Hence, the frequency of each range in the table is as follows:-

Range               Frequency

\(0-4\)                         \(2\)

\(5-9\)                         \(3\)

\(10-14\)                      \(6\)

\(15-19\)                      \(0\)

\(20-24\)                      \(1\)

\(25-29\)                      \(2\)

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The lateral surface area of the prism is 21 ft².

This refers to all of the sides of the object, not including its base and top.  It is measured in square units.

Solving for the lateral surface area of the prism :

The lateral surface area of a rectangular prism can be calculated using the formula:

l =  4ft

w = 3ft

h = 1.5ft

LSA = 2( l + w) h

      = 2(  4ft + 3ft) *1.5ft

      = 14 ft * 1.5ft

      = 21 ft²

Hence, the lateral surface area of the prism is 21 ft².

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High-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

A scatter plot is a graphical representation of data points, with the x-axis representing the independent variable (such as the level of production) and the y-axis representing the dependent variable (such as the cost). Linear cost behavior means that the relationship between the independent and dependent variables can be approximated by a straight line. In other words, as the independent variable increases or decreases, the dependent variable changes proportionally.

To determine if a scatter plot depicts linear cost behavior, you need to visually examine the data points. If the points appear to align closely along a straight line, it indicates a linear relationship. However, if the points are scattered and do not follow a clear pattern, it suggests non-linear cost behavior.

High-low or least squares regression analysis are statistical techniques used to estimate and quantify the linear relationship between variables. These methods help determine the equation of the line that best fits the data points and can be used to predict future values. Therefore, performing these analyses is only meaningful when the scatter plot indicates linear cost behavior.

In summary, high-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

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There are approximately 2425 of those intervals that will contain the population means.

A confidence interval is a range of values that includes a parameter estimate with a certain degree of certainty. A confidence interval is a measure of uncertainty about an estimation procedure, rather than a statement about a parameter. A confidence interval is a specific value or a range of values in statistics that is used to estimate population characteristics.

This is because a 97% confidence interval means that if we were to repeat the sampling process many times, about 97% of the resulting intervals would contain the population mean. In other words, we would expect 97% of the intervals to be "correct" in the long run, while about 3% of them would not contain the population mean.

Therefore, out of the 2500 intervals we compute, we would expect approximately 0.97 x 2500 = 2425 intervals to contain the population mean, and about 0.03 x 2500 = 75 intervals not to contain the population mean. However, it's important to note that the actual number of intervals that contain the population means may vary from this expected value due to random sampling variability.

Where, \(\[\bar{x}\]\) is the sample mean

\(\[\frac{s}{\sqrt{n}}\]\) is the standard error of the mean

zα/2 is the z-score that covers α/2 in the tails of a normal distribution.

As we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample, the proportion of the sample will contain the population means.

Therefore, the number of intervals that will contain the population mean is approximately 2425.

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Answer:

4.4%

Step-by-step explanation:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+  

n

r

​  

)  

nt

Compound interest formula

A=11700\hspace{35px}P=6900\hspace{35px}t=12\hspace{35px}n=365

A=11700P=6900t=12n=365

Given values

11700=

11700=

\,\,6900\left(1+\frac{r}{365}\right)^{365(12)}

6900(1+  

365

r

​  

)  

365(12)

Plug in values

11700=

11700=

\,\,6900\left(1+\frac{r}{365}\right)^{4380}

6900(1+  

365

r

​  

)  

4380

Multiply

\frac{11700}{6900}=

6900

11700

​  

=

\,\,\frac{6900\left(1+\frac{r}{365}\right)^{4380}}{6900}

6900

6900(1+  

365

r

​  

)  

4380

​  

Divide by 6900

1.695652174=

1.695652174=

\,\,\left(1+\frac{r}{365}\right)^{4380}

(1+  

365

r

​  

)  

4380

\left(1.695652174\right)^{1/4380}=

(1.695652174)  

1/4380

=

\,\,\left[\left(1+\frac{r}{365}\right)^{4380}\right]^{1/4380}

[(1+  

365

r

​  

)  

4380

]  

1/4380

Raise both sides to 1/4380 power

1.000120571=

1.000120571=

\,\,1+\frac{r}{365}

1+  

365

r

​  

-1\phantom{=}

−1=

\,\,-1

−1

Subtract 1

0.000120571=

0.000120571=

\,\,\frac{r}{365}

365

r

​  

365\left(0.0001206\right)=

365(0.0001206)=

\,\,\left(\frac{r}{365}\right)365

(  

365

r

​  

)365

Multiply by 365

0.044008415=

0.044008415=

\,\,r

r

4.4008415\%=

4.4008415%=

\,\,r

r

Answer:

4.4%  

Step-by-step explanation:

Answer:

1). t ≥ -\(\frac{3}{2}\)

2). k ≥ \(\frac{16}{3}\)

3). y < -\(\frac{1}{2}\)

4). b > \(\frac{250}{9}\)

5). w ≤ 0

Step-by-step explanation:

1). \(14(\frac{1}{2}-t)\leq 28\)

   \(\frac{14}{14}(\frac{1}{2}-t)\leq \frac{28}{14}\)

   \(\frac{1}{2}-t\leq 2\)

   \(-t\leq 2-\frac{1}{2}\)

   \(-t\leq \frac{3}{2}\)

   t ≥ -\(\frac{3}{2}\)

2). 15k + 11 ≤ 18k - 5

   15k - 18k ≤ -5 - 11

   -3k ≤ - 16

   3k ≥ 16

     k ≥ \(\frac{16}{3}\)

3). 44y > 11 + 88y - 22y

    44y > 11 + 66y

    44y - 66y > 11

    -22y > 11

    22y < -11

    \(\frac{22y}{22}<-\frac{11}{22}\)

    y < \(-\frac{1}{2}\)

4). \(\frac{7}{9}(b - 27) > \frac{49}{81}\)

    \(\frac{7}{9}(b - 27)\times \frac{9}{7} > \frac{49}{81}\times \frac{9}{7}\)

     (b - 27) > \(\frac{7}{9}\)

     b > \(\frac{7}{9}+27\)

    b > \(\frac{250}{9}\)

5). 11w - 8w ≥ 14w

    3w - 14w ≥ 0

    -11w ≥ 0

    w ≤ 0

Answer:

Refer to the attached file

Hope it helps..

Have a great day : )

Answer:

Answer:

d: The graph shifts 3 units up

Step-by-step explanation:

Answer:

Hope this helps.

Answer:

True

Right angles measure 90° . So each vertical angle = 90° and hence they are equal

Step-by-step explanation:

To determine if an element in the list 'mylst' matches the given integer 'key' using a loop, you can use the following code:

```python
found = False

for element in mylst:
   if element == key:
       found = True
       break

if found:
   print("The key value was found in the list.")
else:
   print("The key value was not found in the list.")
```

This code utilizes a for loop to iterate through each element in 'mylst'. If an element matches the 'key' value, the 'found' variable is set to True, and the loop is terminated. The result is then printed accordingly.

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