When the piggy bank was opened, it yielded $5.22 in nickels and pennies. If there were 162 nickels and pennies altogether, how many of each were in the bank? Write your answer in the order of the sample answer: 5 nickels, 6 pennies. PLEASE GIVE AN ACTUALLY ANSWER! Thank you!

Answer:

x = 9

Step-by-step explanation:

30 = 2(x +6)

30 = 2x +12

Subtract 12 from both sides.

18 = 2x

divide both sides by 2.

9 = x

First, we can simplify the equation by dividing both sides by 2:

30/2 = x + 6

This gives us:

15 = x + 6

Now we can solve for x by subtracting 6 from both sides:

15 - 6 = x

Therefore, the solution is:

x = 9.

[tex]D:2x > 0\wedge x+2 > 0\\D:x > 0 \wedge x > -2\\D: x > 0[/tex]

[tex]\log_42x+\log_4(x+2)=2\\\log_4(2x(x+2))=2\\2x^2+4x=4^2\\2x^2+4x-16=0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4[/tex]

[tex]-4\not\in D[/tex]

Therefore [tex]x=2[/tex].

To determine Cody's total revenue if he charges $20 for each mailbox, we need to know the number of mailboxes he sells. Let's denote the number of mailboxes as 'n'.

Cody's total revenue can be calculated by multiplying the price per mailbox ($20) by the number of mailboxes sold (n):

Total revenue = Price per mailbox × Number of mailboxes sold

Total revenue = $20 × n

Therefore, Cody's total revenue will be $20n, where 'n' represents the number of mailboxes he sells.

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The angles in the triangle are as follows:

m∠S = m∠Q = 58°

m∠T = 64°

The unknown angles in the triangle can be found as follows:

In the triangle STQ, ST = TQ and SD is perpendicular to TQ.

Therefore, let's find the unknown angles as follows:

Hence, base on ST = TQ, STQ is an isosceles triangle. Therefore,

m∠S = m∠Q

Therefore,

m∠Q = 180 - 90 - 32

m∠Q = 58 degrees

m∠S = m∠Q = 58 degrees

Finally,

m∠T = 180 - 58 - 58

m∠T = 64 degrees

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Using the given information, the measure of each exterior angle in the polygon is 20°

From the question, we are to determine the measure of each exterior angle in the polygon

Let the number of sides in the polygon be n.

Sum of exterior angles in a polygon = 360°

Thus,

Measure of one exterior angle = 360°/n

From the given information,

The measure of each exterior angle is 12.5% of the measure of each interior angle

The measure of each interior angle = (n - 2)180° / n

Thus,

360°/n = 12.5% of (n - 2)180° / n

360° = 12.5% of (n - 2)180°

Solve for n

360° = 0.125 × (n - 2)180°

360° =  (n - 2)22.5°

360° = 22.5n° - 45°

22.5n° = 360° + 45°

22.5n° = 405°

n = 405°/22.5°

n = 18

Then,

Measure of each exterior angle = 360° / 18

Measure of each exterior angle = 20°

Hence, the measure of each exterior angle is 20°

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The volume of composite solid is 418.67 cm³.

We have to find the volume of Cone and cylinder.

First, Volume of Cone

=  (1/3)πr²h

Given that the radius (r) of the cone is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:

= (1/3) (3.14) (5)² (4)

= 104.67 cm³

Second, Volume of cylinder

= πr²h

Given that the radius (r) of the cylinder is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:

= π (5)² (4)

= 3.14 x 100

= 314 cm³

Thus, the volume of composite solid

= 314 + 104.67

= 418.67 cm³

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For the sample of n sludge specimens is selected and the conclusion and the pH of each one is determined.

The null hypothesis will be rejected in favour of the alternative hypothesis only if sample evidence suggests that H0 is false. If the sample does not strongly contradict H0, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H0.

A) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

B) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

C) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

D) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

E) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.

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The type of correlation that occurs when two variables are statistically correlated due to the influence of a third variable is called a spurious correlation.

A spurious correlation is a type of correlation that occurs when two variables are statistically related to each other, but the relationship is not causal. Instead, the relationship is driven by the influence of a third variable that is related to both variables. This type of correlation can be misleading and can lead to incorrect conclusions if not properly understood.

For example, consider the relationship between ice cream sales and violent crime. Studies have found a positive correlation between these two variables, meaning that as ice cream sales increase, so do violent crimes. However, it is unlikely that there is a causal relationship between these two variables. Instead, the real cause of the correlation is likely the temperature. As the temperature increases, people are more likely to buy ice cream and to be out and about, which increases the opportunity for violent crime to occur. Thus, the temperature is the third variable that is driving the spurious correlation between ice cream sales and violent crime.

It is a type of correlation where there is no causal relationship between the two variables that are correlated. Instead, the correlation is driven by the influence of a third variable that is related to both variables. In the example given, the correlation between ice cream sales and violent crimes is spurious, as the real cause of the correlation is the temperature, which influences both variables.

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The an 18-year-old homeless Floridian would be considered at the 22nd percentile in the distribution of ages of homeless Floridians.

the social worker estimated that 78% of the homeless population in Florida in 2018 were age 18 and up, which means that 22% of the homeless population were under 18 years old. Therefore, an 18-year-old would be at the 22nd percentile in the age distribution of homeless Floridians.

based on the given information, an 18-year-old homeless Floridian would be at the 22nd percentile in the age distribution of homeless Floridians.

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The most appropriate method to use for estimating the percent of horseshoe crabs longer than 35 centimeters in a certain area would be a one-sample z-interval for a population proportion (Option C).

In this scenario, the biologists want to estimate a percentage or proportion (percent of crabs longer than 35 centimeters) for a specific population (horseshoe crabs in a certain area). A one-sample z-interval for a population proportion is used when estimating a single population proportion based on a random sample. It allows for determining a confidence interval for the true proportion in the population using the sample data.

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Answer:

(C) 297

Step-by-step explanation:

Write a proportion. 45 miles is to 5 gallons as x miles is to 33 gallons.

45 / 5 = x / 33

9 = x / 33

x = 297

Out of the remaining 85 burros, 32 burros are expected to stop before the finish line.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

3 out of the 5 + 3 = 8 burros stopped before the finishing line, hence the probability is given as follows:

p = 3/8.

Out of 85 burros, the expected number to stop before the finish line is given as follows:

3/8 x 85 = 32 burros. (rounded up).

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10 liters of water was drained out of the tank in one minute and it would take 80 minutes to completely drain the water

This is the slope of the graph

From the graph, we have

(x, y) = (0, 800) and (40, 400)

So, we have

Slope = (400 - 800)/(40 - 0)

Evaluate

Slope = -10

This means that 10 liters of water was drained out of the tank in one minute

From (a), the equation of the line would be

y = -10x + 800

When the water is completely out, we have

-10x + 800 = 0

So, we have

x = 80

This means that it would take 80 minutes

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Answer:

192.17 mi

Step-by-step explanation:

Let x be the number of one hour sessions that Mrs. B teaches and let y be the number of half hour sessions that she teaches per week. Then we can write the following system of inequalities to represent her goals:

60x + 40y > 800 (She hopes to make more than $800 tutoring)

x + y <= 12 (She can work a maximum of 12 hours per week)

To determine how many one hour sessions and half hour sessions she can teach, we need to graph these inequalities on a coordinate plane. The graph should show the shaded region that satisfies both inequalities.

To graph the inequality 60x + 40y > 800, we can first rewrite it as:

3x + 2y > 40

Then we can graph the line 3x + 2y = 40 by plotting the points (0,20) and (13.33,0) and drawing a line through them. Since we want to graph the inequality 3x + 2y > 40, we need to shade the region above the line.

To graph the inequality x + y <= 12, we can simply graph the line x + y = 12 by plotting the points (0,12) and (12,0) and drawing a line through them. Since we want to graph the inequality x + y <= 12, we need to shade the region below the line.

The shaded region that satisfies both inequalities is the region that is above the line 3x + 2y = 40 and below the line x + y = 12. This region is a triangle with vertices at (0,12), (8,4), and (13.33,0).

To determine if Mrs. B can teach 5 one hour sessions and 14 half hour sessions, we can plug these values into the inequalities and see if they are satisfied:

60(5) + 40(14) = 860 > 800 (This inequality is satisfied)

5 + 14 = 19 <= 12 (This inequality is not satisfied)

Since the second inequality is not satisfied, it is not possible for Mrs. B to teach 5 one hour sessions and 14 half hour sessions.

Answer:

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

Let the dimensions be x and y.

The area is:

When sides have changed we get:

The new area is:

The difference in areas is:

It represents 17% increase.

because their sides were corresponding.

answers:

1. aas (g).

2. sas (h).

3. sss (n).

4. asa (s).

5. hl (c).

6. none - aaa (t).

7. asa (0).

8. none - ssa (d).

9. aas (i).

10. sas (w).

11. sss (p).

12. hl (r).

13. asa (e).

Population proportion (claim): p = 0.85

Sample proportion: [tex]\hat p[/tex]= 19/25

What is proportion?

In statistics, proportion typically refers to the proportion or percentage of individuals or items in a population that have a specific characteristic or belong to a certain category.

In this scenario, the population proportion refers to the proportion of all Prime members' packages that arrive within two business days. The claim made by Amazon is that this population proportion is 85%.

Let's denote the population proportion as p.

a. The population proportion:

p = 0.85

The sample proportion, on the other hand, refers to the proportion of packages that arrived within two business days among the 25 students in the random sample. We can calculate the sample proportion using the number of students who claimed their packages arrived within two business days.

Let's denote the sample proportion as [tex]\hat p[/tex] (pronounced "p-hat").

Given:

Number of students in the sample (n) = 25

Number of students who claimed their packages arrived within two business days (x) = 19

b. The sample proportion:

[tex]\hat p[/tex] = x / n

[tex]\hat p[/tex] = 19 / 25

Therefore, the sample proportion is 19/25.

To summarize:

Population proportion (claim): p = 0.85

Sample proportion: [tex]\hat p[/tex] = 19/25

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P(A AND B) is approximately 0.101 (rounded to three decimal places).

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

To find P(A AND B), we can use the conditional probability formula:

P(A AND B) = P(A|B) * P(B)

Given:

P(A|B) = 0.22

P(B) = 0.46

Plugging in the values:

P(A AND B) = 0.22 * 0.46

Calculating the result:

P(A AND B) = 0.1012

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Answer:

Step-by-step explanation:

[tex](7+x)^5[/tex]

The fourth choice in this scenario is the Type II error: (d) Using the sample mean, the owner determines that the average weight of all the banana bunches is more than 3.54 pounds even though the real average weight is lower.

When the null hypothesis—in this case,

The average weight of the banana bunches is 3.54 pounds—is not accepted despite being erroneous, a Type II mistake takes place.

In other words, despite the cargo of bananas not meeting the requisite weight criteria, the owner fails to reject it. In this case, the owner may experience a loss in sales or reputation as a result of the poor quality of the bananas, as well as losses from selling the underweight bananas at a loss or even throwing them away.

The probability of making a Type II error can be minimized by increasing the sample size or decreasing the significance level (alpha level) of the test. However, a Type II error can never be completely eliminated.

Therefore, the correct option is d.

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Answer:

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

The first step involves addition of 7 to both sides and the second step involves division of both sides by 9.

They indicate the addition and division property of equality respectively.

Therefore correct choice is A.

[tex]|\Omega|=6+4+2=12\\|A|=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}\approx33.3\%[/tex]

Answer:

Step-by-step explanation: 6 + 4 + 2 = 12 (denominator)

Put 4 (blue beads) in numerator

4/12 reduces to 1/3

Final answer is 1/3

The probability that a student who passed the test did not complete the homework is 1 / 6.

This is a conditional probability problem and we are looking for the probability that a student who passed the test did not complete the homework.

Assuming event A is the event that a student passed the test and B is  event that a student completed the assignment.

We have :

P ( B' | A ) = P ( A ∩ B ' ) / P (A)

P ( B' | A ) = ( 3 / 27 ) / ( 18 / 27 )

P ( B' | A ) = 3 / 18

P (B' | A ) = 1 / 6

In conclusion, the probability that a student who passed the test did not complete the assignment is 1/6.

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The best estimate of the number of raccoons in the area is approximately 71.

The best estimate of the number of raccoons in the area can be obtained using the mark and recapture method, also known as the Lincoln-Petersen index.

The formula for the Lincoln-Petersen index is:

Estimated population size = (Number of marked individuals in first sample * Total number of individuals in second sample) / Number of marked individuals recaptured in second sample

In this case, 16 raccoons were initially captured and tagged, and in the subsequent sample of 40 raccoons, 9 were found to be tagged.

Using the formula, the estimated population size would be:

Estimated population size = (16 * 40) / 9 = 71.11

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The factor that -8 - 7i should be multiplied by to find the quotient is 1 + 2i and the quotient is (-22 - 23i) / 5.

When dividing complex numbers of the form a + bi by another complex number of the form c + di, we use the following method:

Multiplying both the numerator and denominator by the conjugate of the denominator, c - di, we get:

(a + bi)(c - di)/(c + di)(c - di) = [(ac + bd) + (bc - ad)i]/(c² + d²)

where a, b, c, and d are real numbers and i is the imaginary unit with the property i² = -1.

In the given question, the denominator is 1 - 2i, so its complex conjugate would be 1 + 2i. Therefore, we need to multiply -8 - 7i by 1 + 2i in both numerator and denominator to get the quotient: (-8 - 7i)(1 + 2i) / (1 - 2i)(1 + 2i) = (-8 - 23i - 14) / (1 + 4) = (-22 - 23i) / 5

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We can use the distance formula to find the distances between the fire hydrants and determine whether they form a right triangle. The value of y is 4.

The distance between (0,0) and (2,5) is:

√((2-0)² + (5-0)²) = √29

The distance between (0,0) and (7,y) is:

√((7-0)² + (y-0)²) = √(49 + y²)

The distance between (2,5) and (7,y) is:

√((7-2)² + (y-5)²) = √(25 + (y-5)²)

If these distances form a right triangle, then the Pythagorean theorem must be satisfied:

(√29)² + (√(49 + y²))² = (√(25 + (y-5)²))²

Simplifying this expression, we get:

29 + 49 + y² = 25 + (y-5)²

Expanding the square on the right-hand side, we get:

29 + 49 + y² = 25 + y² - 10y + 25

Simplifying this expression, we get:

y = 4

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Answer:58

Step-by-step explanation:

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

To find the range of the following set of numbers: 68, 56, 40, 10, 51, 15

First, we need to find the largest and smallest numbers in the set.

The largest number is 68 and the smallest number is 10.

So, the range is:

68 - 10 = 58

Therefore, the range of the set of numbers is 58.