Question 12 (16 points) Below is a sample of times (in minutes) that it takes students to complete an exam. Data: 23.2, 50.1, 57.6, 54.5, 52.7, 55.6, 52.9, 58.3, 19.5, 55.6, 58.3 Calculate the five nu

Answer:

\( \boxed{ \bold{ \sf{x = 16}}}\)

\( \boxed{ \bold{ \sf{m < AFD = 82}}}\)

Step-by-step explanation:

\( \sf{5x + 18 = 3x + 50}\)

( Being vertically opposite angles)

Vertically opposite angles are always equal.

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S and change it's sign

⇒\( \sf{5x - 3x = 50 - 18}\)

Collect like terms

⇒\( \sf{2x = 50 - 18}\)

Subtract 18 from 50

⇒\( \sf{2x = 32}\)

Divide both sides of the equation by 2

⇒\( \sf{ \frac{2x}{2} = \frac{32}{2} }\)

Calculate

⇒\( \sf{x = 16}\)

The value of x is 16

Now, let's find value of m<AFD :

\( \sf{m < afd + 5x + 18 = 180}\) ( sum of angle in straight line )

plug the value of x

⇒\( \sf{m < AFD + 5 \times 16 + 18 = 180}\)

Multiply the numbers

⇒\( \sf{m < AFD + 80 + 18 = 180}\)

Add the numbers

⇒\( \sf{m < AFD + 98 = 180}\)

Move constant to R.H.S and change it's sign

⇒\( \sf{m < AFD = 180 - 98}\)

Subtract 98 from 180

⇒\( \sf{m < AFD = 82}\)

Value of m<AFD = 82

Hope I helped!

Best regards!!

Answer:

f(x)=(x+2)^2+37

Step-by-step explanation:

Got it right on Khan :)

The quadratic function f(x) = x² + 4x + 41 is converted into square form is f(x) = (x + 2)² + 37.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The quadratic function is given below.

f(x) = x² + 4x + 41.

The quadratic function is converted into square form by adding and subtracting the square of the half of the coefficient of x.

f(x) = x² + 4x + 41

Transform into square form. Then the quadratic function will be

f(x) = (x² + 4x + 4) + 41 – 4

f(x) = (x + 2)² + 37

The quadratic function f(x) = x² + 4x + 41 is converted into square form is f(x) = (x + 2)² + 37.

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Probability of the person has the diseases and the test result is positive = 1/90 = 0.011

Probability  refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.

Given, percentage of people who have disease and test result positive =90

percentage of people who has not disease but test result positive =3.1

Suppose 6.0 percent of population are infected

Now, probability of a  randomly selected person  who has diseases and test positive

                          = 1/90

                       =   0.011

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the null hypothesis for the given t-test\(`[h, p, 0] = ttest(morningsections, eveningsection)`\)

In the t-test formula for hypothesis testing, the null hypothesis states that there is no difference between the two groups being tested. Therefore, for the given t-test below:

`[h, p, 0] = ttest(morningsections, eveningsection)`,

the null hypothesis is that there is no significant difference between the average bedtimes of students in morning sections versus evening sections.

To explain further, a t-test is a type of statistical test used to determine if there is a significant difference between the means of two groups. The formula for a t-test takes into account the sample size, means, and standard deviations of the two groups being tested. It then calculates a t-score, which is compared to a critical value in order to determine if the difference between the two groups is statistically significant.

In this case, the two groups being tested are morning sections and evening sections, and the variable being measured is the average bedtime of students in each group. The null hypothesis assumes that there is no significant difference between the two groups, meaning that the average bedtime of students in morning sections is not significantly different from the average bedtime of students in evening sections.

The alternative hypothesis, in this case, would be that there is a significant difference between the two groups, meaning that the average bedtime of students in morning sections is significantly different from the average bedtime of students in evening sections. This would be reflected in the t-score obtained from the t-test, which would be compared to the critical value to determine if the null hypothesis can be rejected or not.

In conclusion, the null hypothesis for the given t-test\(`[h, p, 0] = ttest(morningsections, eveningsection)`\) is that there is no significant difference between the average bedtimes of students in morning sections versus evening sections.

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The values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

We can use the logarithm properties to find the value of log57 given that log75 is 0.83.

One of the logarithm properties states that:

log(a * b) = log(a) + log(b)

Using this property, we can express log57 in terms of log75:

log57 = log(5 * 3 * 19)

Now, we can use the fact that log75 is 0.83 to find log5, log3, and log19, and then add them together to get the value of log57:

log57 = log(5 * 3 * 19)

log57 = log5 + log3 + log19

However, since the values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

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The equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

To find log57 using the given information log75 = 0.83, we can use the change of base formula:  

if log75 = 0.83, then log57 ≈ 0.827. To find log57 using the given information log75 = 0.83, we can use the change of base formula:log_b(a) = log_c(a) / log_c

Here, we want to find log57 (log_7(5)) using the given information log75 (log_5(7)).

We can rewrite the change of base formula as:log_7(5) = log_x(5) / log_x(7)We know that log_5(7) = 0.83,

so we can substitute this value into the equation:log_7(5) = log_x(5) / 0.83

Now we can use any common base, like base 10 or base e, to find the value of log_7(5). Let's use base 10:log_7(5) = log_10(5) / log_10(7)Now

we can calculate the values of log_10(5) and log_10(7) using a calculator:log_10(5) ≈ 0.69897log_10(7) ≈ 0.84510

Now substitute these values back into the equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

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The method of periodization that an athlete performs is  traditional periodization method.

Given,

An athlete perform five sets of five repetitions at 90% of 1rm on the first day of the week, five sets of fourteen repetitions at 85% of 1rm on the next training day, and five sets of two repetitions at 62.5%of 1rm on the last training day of the week;

Here,

The example above, where the percentage of one-repetition maximum (1RM) decreases as the training day progresses, is essentially a traditional periodization method.

As a result, during the course of the training cycle, the athletes' completed work gradually grows. As a result, as the load increases over time, there is a corresponding decrease in volume.

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The circumference of the circle is 69.08 inches.

Circumference is the distance around the outside of a circle.

We can use the formula C = πD or C = 2πr to find the circumference.

- Given radius = 11 inches, we can find the circumference of a circle as follows:

C = πD or C = 2πr

We are given that 11 inches is the radius (r) of a circle.

So, we could use C = 2πr where r is the radius of the circle.

Now we can use C = 2πr to find the circumference of the circle

(using π = 3.14):

C = 2πr = 2π × 11 inches

= 69.08 inches

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Answer:

z

Step-by-step explanation:

hope it will help full

is it right

Answer:24.1 feet long

Step-by-step explanation:

The equivalent fractions for 2/3 is (3×2)/(3×3) = 6/9 and for  5/12 is (4×5)/(4×12) = 20/48.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The equivalent fraction for 2/3 is (3×2)/(3×3) = 6/9.

The equivalent fraction for 5/12 is (4×5)/(4×12) = 20/48.

We have to multiply the same number to both the numerator and denominator to get equivalent fractions.

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Answer:

number of apples in each bag

The sequence is arithmetic and the common difference is -8.

The term number 24 is:

A(24) = -206

To check if a sequence is arithmetic, take the difference between the consecutive terms, you should get the same value for all the cases.

Here we have:

-22, -30, -38, -46, ...

The differences give:

-30 + 22 = -8

-38 + 30 = -8

-48 + 38 = -8

We get the same thing in all, so the sequence is arithmetic, and the common difference is -8.

The n-th term of this sequence will be:

A(n) = -22 + (-8)*(n - 1)

Then the 24th term is:

A(24) = -22 + (-8)*(24 - 1)= -206

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Answer:

9y+19

Step-by-step explanation:

7y+9+2y+10

Combine like terms

7y+2y    +9+10

9y            +19

Answer:

see explanation

Step-by-step explanation:

Consider perfect squares on either side of 73, that is

64 < 73 < 81 , then

\(\sqrt{64}\) < \(\sqrt{73}\) < \(\sqrt{81}\) , that is

8 < \(\sqrt{73}\) < 9

Answer:

8<square root of 73<1

i think this are the integers that are closest to the number in the middle.

Answer:

the battery rate is 6.5

Step-by-step explanation:

Answer:

2 percent per minute

Step-by-step explanation:

The rate at which the battery was charged is equivalent to the rate of change of this relationship. In linear relationships, the rate of change is represented by the slope of the line. We can calculate this slope from any two points on the line. Two points whose coordinates are clearly visible from the graph are (0,40) and (5,50). Now, to find the slope, let's take the ratio of the corresponding differences in the y-values and the x-values: 50-40/5-0=10/5=2. The slope of the line is 2, which means the battery was charged at a rate of 2 percent per minute.

Answer:

C

Step-by-step explanation:

Answer:

x-0.25 is the answer for the above expression

The value of the median, it stays the same. Option C

The value of the mean, It decreases by 10.9. Option A

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

From the information given, we have that;

216, 256, 262, 276, 277, 305, 410

If 410 becomes 33

Then, we have;

Mean = 216+ 256 + 262 + 276 + 277+  305 + 333/6

Mean = 1926/7 = 275.1

Median refers to the middle number in a given set of data arranged from the least to the greatest

Median = 276

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Answer:

50 degrees, 40 degrees

Step-by-step explanation:

3x-25+x+15=90                       Complementary angles add up to 90 degrees

4x-10=90

4x=100

x=25

75-25=50 and 25 plus 15=40  50+40=90

x=25°

There are two angles that can form:

• Supplementary Angles: if both angles are added = 180 °

• Complementary Angles: if both angles are added = 90 °

(3x-25)+((x+15)=90

4x-10=90

4x=100

x=25°

As per the function represented by the table, the correct function notation is f(5) = 9.

Given a function represented by a table is shown as follows:

x| 2 | 5 | 9

y| 9 | 14| 5

We can say that the ordered pair given in the bottom row can be written using function notation as f(5) = 9.

Function notation is a method to represent functions, and it is usually used in mathematics to make it easier to work with functions.

It helps to identify the input, the function, and the output of a function.

Using function notation:In function notation, the input is represented by the variable x, and the output is represented by the variable y.

Therefore, we can say that f(x) = y.

Using the table, we can see that when x = 5, y = 14.

So, f(5) = 14 is the correct answer to the given question.

Here, we see that the x and y coordinates are swapped from what we are used to.

The correct function notation is f(5) = 9.

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Answer

5.9

12.95*2=25.9

25.9-20

The 74th percentile of the sample mean for the number of pets per household is approximately 3.08.

To find the 74th percentile of the sample mean when the mean number of pets per household is 2.96 with a standard deviation of 1.4 and a sample size of 52 households, you can follow these steps:

1. Determine the standard error of the sample mean.

The standard error (SE) is calculated by dividing the population standard deviation by the square root of the sample size:
SE = σ / √n
SE = 1.4 / √52
SE ≈ 0.194

2. Determine the z-score associated with the 74th percentile.

You can use a z-table or a calculator to find the z-score that corresponds to a cumulative probability of 0.74. The z-score is approximately 0.63.

3. Calculate the sample mean associated with the 74th percentile by using the z-score, the population mean, and the standard error:
Sample mean = μ + z * SE
Sample mean = 2.96 + 0.63 * 0.194
Sample mean ≈ 3.08

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Answer:3.46 km

Step-by-step explanation:

Given

shape of hill \(y=-2(x-3)^2+6\)

at the bottom y=0 i.e.

\(0=-2(x-3)^2+6\\(x-3)^2=3\\x-3=\pm\sqrt{3}\\x=3\pm\sqrt{3}\)

width of the bottom

\(3+\sqrt{3}-[3-\sqrt{3}]=2\sqrt{3}\ km\ or\ 3.46\ km\)

Answer: There is no mode.

Step-by-step explanation:

The mode is the number in a data set that occurs most frequently. Count how many times each number occurs in the data set. The mode is the number with the highest tally. It's ok if there is more than one mode. And if all numbers occur the same number of times there is no mode.

Hope this helps!

Answer:

R 694.4

Explanation:

simple interest = \(\sf{\dfrac{PRT}{100}\) → \(\sf \dfrac{560*8*3}{100}\) → R 134.4

where p refers to principal, r refers to rate, t refers to time.

total money:

invested money + simple interest

R 134.4 + R 560 → R 694.4

Answer:

R 694.40

Step-by-step explanation:

Simple interest formula:

A = P(1 + rt)

where A is the final amount, P is the initial principal balance, r is the annual interest rate (in decimal format), and t is time (in years)

Given:

⇒ A = 560(1 + 0.08 · 3)

⇒ A = 560(1.24)

⇒ A = 694.40

The proportion taken by John 3:4 = 5:12 is correct.

The term called proportion in math is defined as the values of the proportion that are close to each other when written in ratio form using a colon.

Here we know that the  a 3-4-5 right triangle and a 5-12-13 right triangle are set by John.

And the taken proportion is written as,

=> 3:4 = 5:12

Here we have to use the Pythagoras theorem to verify this one, then we get,

=> 3² + 4² = 5²

=> 9 + 16 = 25

=> 25 = 25

Now, we have to take the other values and verify that one also,

=> 5² + 12² = 13²

=> 25 + 144 = 169

=> 169 = 169

Therefore the proportion is correct.

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