A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 7 centimeters long, and the height of the equilateral triangle is 6.1 centimeters. The pyramid's slant height is 9 centimeters. What is its surface area?​

Answer:

a) Thin mints = 1.885 radians

b) Savannah smiles cookies = 0.332 radians

Step-by-step explanation:

To convert an angle from degree to radians, the formula is given as :

x ° × π/180 = radians

Where x = angle to be converted

From the diagram we are to convert Thin mints and Savannah cookies to radians

a) Thin mints = 108°

Converting to radians

= 108° × π/180

= 1.8849555922 radians

Approximately = 1.885 radians

b) Savannah smiles cookies = 19°

Converting to radians

= 19° × π/180

= 0.331613 radians

Approximately = 0.332 radians

Answer:

Each individual lost 6 pieces

Step-by-step explanation:

Initially, there were 32 pieces

After a while, 20 was left

The number of pieces lost will be 32-20 = 12 pieces

We are told that equal number of pieces were lost

So the number of pieces lost per individual will be:

12/2 = 6 pieces

Answer:

Step-by-step explanation:

I'm not sure how correct I am about these questions, but this is what I got:

13.x=-9

14.x=8

15.x=-2

16.x=5

17.x=-1

18.x=1.5

Answer:

the answer is d aka V=2/9s3

Step-by-step explanation:

Answer:

the answer is d aka V=2/9s3

Step-by-step explanation:

i just took the test and got it right

Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

3) answer 68 feet and 4) answer 38

Step-by-step explanation:

you just need to multiply by 2 easy itsn't it

Answer:

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

We see x - 2 is the common factor in the given expression.

Simplify as:

Answer:

10x - 20

Step-by-step explanation:

distribute the 3 and the 7 into the parentheses, getting you to (3x - 6) + (7x - 14), from there you should be able to just combine the like terms getting you to 10x - 20.

Therefore, the line integral is:

∫c xy^4 ds = 125∫[0,pi] cos(t)sin^4(t) dt = 125(48/5) = 1200

The right half of the circle x^2 + y^2 = 25 can be parameterized as c(t) = (5cos(t), 5sin(t)) for t in [0, pi], where the orientation is counterclockwise.

The line integral of xy^4 along c is given by:

∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt

where ||c'(t)|| is the magnitude of the derivative of c with respect to t.

We have:

c'(t) = (-5sin(t), 5cos(t))

||c'(t)|| = sqrt[(-5sin(t))^2 + (5cos(t))^2] = 5sqrt(sin^2(t) + cos^2(t)) = 5

So the line integral becomes:

∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt

= 5∫[0,pi] 25cos(t)sin^4(t) dt

= 125∫[0,pi] cos(t)sin^4(t) dt

To evaluate this integral, we can use integration by substitution. Let u = sin(t), then du/dt = cos(t) and dt = du/cos(t). So we have:

∫cos(t)sin^4(t) dt = ∫u^4 du/cos(t) = ∫u^4 sec(t) du

We can evaluate this integral as follows:

∫u^4 sec(t) du = sec(t)u^5/5 - 2/5 ∫u^2 sec(t) du

= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 4/15 ∫u^2 du

= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3 + C

where C is the constant of integration.

Substituting back u = sin(t) and integrating over [0,pi], we obtain:

∫[0,pi] cos(t)sin^4(t) dt

= [sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3]_0^pi

= (0 - 0 + 2/5(5^3)) - (1/5 - 0 + 0)

= 48/5

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Answer:

5.5 rings

Step-by-step explanation:

Now I don't really know if this is right but to get the answer we need to know how much ounces of gold the jeweler need to make a ring and that would be 7.7 ounces of gold. Than divide 42.35 ounce by 7.7 ounces which would get you 5.5 ounces. Hopefully this helped :)

Answer:

5 rings

Step-by-step explanation:

Hope this helps

To find the cost for 3 tickets at the same rate, we can set up a proportion using the given information:

Cost of 5 tickets / Number of tickets = Cost of 3 tickets / Number of tickets

Let's plug in the values we know:

$13.80 / 5 = Cost of 3 tickets / 3

To find the cost of 3 tickets, we can cross-multiply and solve for it:

($13.80 * 3) / 5 = Cost of 3 tickets

$41.40 / 5 = Cost of 3 tickets

$8.28 = Cost of 3 tickets

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Answer:

9

Step-by-step explanation:

;)

Answer:

5! HOPE I HELPED

Step-by-step explanation:

The equation that would give the solution of  x ≤ 4 is -2x ≤-8

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

the equation is given as -2x ≤-8. We are to solve the inequality so as to get the value of x

we are to divide through -2x ≤-8 by -2

-2x / -2 ≤ -8 / -2

x ≤ 4

the other parts of the question are not clearly stated

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Step-by-step explanation:

Yes, the mysteries equal 0.06 of the total books.

Marcella said that the mysteries equal 0.06 of the total books.

To check the mysteries equal 0.06 of the total books is correct or not.

We can follow these steps:

1. Identify the total number of books and the number of mysteries: Marcella read 100 books, and 60 of them were mysteries.

2. Calculate the fraction of mysteries: Divide the number of mysteries (60) by the total number of books (100) to find the fraction of mysteries.

3. Compare the fraction with Marcella's claim: If the calculated fraction equals 0.06, then she is correct.

Now let's perform the calculations:

60 mysteries ÷ 100 total books = 0.6

Since 0.6 ≠ 0.06, Marcella's claim that the mysteries equal 0.06 of the total books is incorrect. In reality, mysteries make up 0.6 or 60% of the total books she read.

A model to support this answer could be a pie chart, where the circle represents the 100 books, and the mysteries portion is shaded in. By dividing the circle into 10 equal sections, the mysteries would fill 6 of those sections, which represents 60% of the total books.

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Answer: 173.82cm^2

Step-by-step explanation:

The point will be inverted when (6,-2) is rotated 90° counterclockwise i.e., the new point will be (-2,6).

It is given that a point (6,-2) is rotated 90° counterclockwise about origin.

We have to find the new point after rotation.

What do you mean by rotation counterclockwise ?

If something is moving counterclockwise that meant it is moving in the opposite direction to the direction in which the hands of a clock move.

As per the question ;

A point (6,-2) is rotated 90° counterclockwise about origin.

Let's assume (6,-2) = (x , y)

If we rotate it 90°counterclockwise ; then the point will be inverted ; i.e.,

(x , y ) ⇒ ( y , x)

So ;

(6 , -2) = (-2,6)

So ;

The new point will be ;

= (-2 , 6)

Thus , the point will be inverted when (6,-2) is rotated 90° counterclockwise i.e., the new point will be (-2,6).

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Question 1: B - The p-value is 0.0062.  Question 2: B - p-value=0.0228; we reject the null hypothesis. Question 3: C - This is a lower-tail test where the sample test statistic (z-value) is -3. Question 4: C - The critical values are ±1.96. We do not reject the null hypothesis.

Question 1:

To test whether the average weight of Kellogg's cereal boxes is greater than 500 grams, we can perform a one-sample t-test. Given a sample of 25 cereal boxes with a sample mean of 525 grams, a standard deviation of 50 grams, and assuming a normal distribution, we can calculate the test statistic.

The test statistic (t-value) can be calculated using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

In this case, the hypothesized mean is 500 grams, the sample mean is 525 grams, the sample standard deviation is 50 grams, and the sample size is 25. Plugging these values into the formula, we get:

t = (525 - 500) / (50 / √25) = 25 / 10 = 2.5

To determine the p-value, we compare the t-value to the t-distribution with (n-1) degrees of freedom. In this case, the degrees of freedom is 25-1=24. By looking up the t-value of 2.5 in the t-distribution table (or using statistical software), we find that the p-value is 0.0062.

Since the p-value (0.0062) is less than the significance level of 0.05, we reject the null hypothesis. Therefore, we have evidence to suggest that the mean weight of all Kellogg's cereal boxes is larger than 500 grams.

Question 2:

To test the claim that children are spending more than 3 hours a day on their smart phones or tablets, we can perform a one-sample t-test. Given a sample of 25 children with a mean of 3.5 hours, a population standard deviation of 1.25 hours, and a 1% significance level, we can calculate the test statistic.

The test statistic (t-value) can be calculated using the formula mentioned earlier. Plugging in the values, we get:

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

t = (3.5 - 3) / (1.25 / √25) = 0.5 / 0.25 = 2

To find the p-value, we compare the t-value of 2 to the t-distribution with (n-1) degrees of freedom. In this case, the degrees of freedom is 25-1=24. By looking up the t-value of 2 in the t-distribution table or using statistical software, we find that the p-value is 0.0228.

Since the p-value (0.0228) is less than the significance level of 0.01, we reject the null hypothesis. Therefore, we have evidence to suggest that children are spending, on average, more than 3 hours on their smart devices.

Question 3:

To test the claim that the average adult listens to the radio less than 20 hours per week, we can perform a one-sample z-test. Given a sample of 36 individuals with a mean of 18 hours, a population standard deviation of 4 hours, and a 5

% significance level, we can calculate the test statistic.

The test statistic (z-value) can be calculated using the formula:

z = (sample mean - hypothesized mean) / (population standard deviation / √sample size)

Plugging in the values, we get:

z = (18 - 20) / (4 / √36) = -2 / (4/6) = -3

Since this is a lower-tail test, we compare the z-value of -3 to the standard normal distribution. By looking up the z-value of -3 in the standard normal distribution table or using statistical software, we find that the p-value is very small (approximately 0.0013).

Since the p-value (0.0013) is less than the significance level of 0.05, we reject the null hypothesis. Therefore, we have evidence to suggest that the average adult listens to the radio less than 20 hours per week.

Question 4:

The correct answer is C. The critical values are ±1.96. We do not reject the null hypothesis.

To test the claim that 80 Kleenex tissues is the average number of tissues used during a cold, we can perform a one-sample z-test. Given a sample of 100 Kleenex users with a sample mean of 82, a population standard deviation of 18, and a significance level of 5%, we can calculate the test statistic.

The test statistic (z-value) can be calculated using the formula mentioned earlier. Plugging in the values, we get:

z = (sample mean - hypothesized mean) / (population standard deviation / √sample size)

z = (82 - 80) / (18 / √100) = 2 / (18/10) = 2 / 1.8 = 1.1111...

To determine the critical values for a two-tailed test at a 5% significance level, we look at the standard normal distribution table or use statistical software. The critical values are ±1.96.

Since the calculated z-value of 1.1111... falls within the range of -1.96 to 1.96, we do not reject the null hypothesis. Therefore, we do not have sufficient evidence to suggest that the average number of tissues used during a cold is different from 80.

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The slope of the line is five (5).

Given the following data;

To find the slope of the line;

We know that the line graphed on a coordinate plane is represented by the relationship between x and y.

Also, we can deduce from the sentence that the value of y is increased by 5 whenever there is an increase in the value of x.

Thus, when;

Mathematically, the slope of a line is given by the formula;

\(Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the points into the formula, we have;

\(Slope. \;m = \frac{10 - 5}{2 - 1}\\\\Slope. \;m = \frac{5}{1}\\\\\)

Slope, m = 5

Therefore, the slope of the line is five (5).

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The total change in the amount of water in the pool is 288 gallons.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Here, Rate of water pumped into her pool = 6 gallons / minute.

          Total Duration = 48 minutes

Total amount of water = Rate X Time

                                     = 6 X 48

                                     = 288 gallons

Thus, the total change in the amount of water in the pool is 288 gallons.

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Amanda's mistake is that she incorrectly calculated the center; the center is (-1, 3)

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

(x + 1)² + (y - 3)² = 9

A circle equation is represented as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

Using the above as a guide, we have the following:

Center = (-1, 3)

Radius = 3

This means that Amanda's mistake is that she incorrectly calculated the center; the center is (-1, 3)

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By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The three sides of a triangle are consecutive if and only if they are represented by three consecutive natural numbers. The perimeter is the sum of the three side lengths, whose formula is presented below:

x + (x + 1) + (x + 2) = 141

3 · x + 3 = 141

3 · (x + 1) = 141

x + 1 = 47

x = 46

By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The statement is complete, the correct statement is the following:

The triangle has three consecutive sides and its perimeter is 141 centimeters. Work out the value of each side.

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The profit made as of investor borrows $100 is $25.

Investing in foreign currencies can be a profitable venture, but it comes with a certain level of risk.

If an investor borrows $100, converts it to pesos, and invests the pesos in Mexico for one year, the profit made is $25.

This is calculated by borrowing $100 and converting it to 625 pesos at the spot rate of 6.25 pesos per dollar.

The 625 pesos are then invested in Mexico for a year at a 45% interest rate, resulting in 281.25 pesos.

The 281.25 pesos are then converted back to dollars at the forward rate of 7.25 pesos per dollar, resulting in $38.75.

The resulting profit is $38.75 - $100 = -$61.25.

Investing in foreign currencies is not without its risks.

When investing in foreign currencies, the exchange rate can change drastically over short periods of time, resulting in losses or gains.

Additionally,

The interest rate in the country of investment can also change, resulting in different levels of returns.

The profit made if an investor borrows $100, converts to pesos and invests in Mexico for a year is $25.

The calculation is as follows:

Borrow $100 and convert to pesos:

100 x 6.25 = 625 pesos

Invest 625 pesos in Mexico for one year:

625 x 45% = 281.25 pesos

Convert 281.25 pesos back to dollars at the forward rate:

281.25 / 7.25 = $38.75

Profit = $38.75 - $100 = -$61.25

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The values in the missing observation are:

X1    X2

76 22  

82 25

91 32

101    41

88 28

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x1 x2

76 22  

82 __

91 32

__    41

88 28

The difference between each row are:

76 - 22 = 54

82 - 25 = 57

91 - 32 = 59

101 - 41 = 60

88 - 28 = 60

We see that,

57 - 54 = 3

59 - 57 = 2

60 - 59 = 1

60 - 60 = 0

So,

The difference between the numbers is consecutive as 3, 2, 1, 0.

Thus,

The missing values of X1 and X2 are 101 and 25.

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Answer:

Step-by-step explanation:

Find the GCF:

12, 24, 36

8, 16, 24, 32

GCF is 24

The lowest amount of boxes the teacher could buy would be 2 boxes of Rulers and 3 boxes of Protractors. I hope this helped