A museum gift shop manager wants to put 1,578 polished rocks into small bags to sell as souvenirs.If the shop manager wants to put 15 rock in each bag,how many complete bags can be filled?How many rocks will be left over

Answer:

The arcs are not congruent which makes the statement false.

Step-by-step explanation: Congruent means equal to my understanding.

Final answer:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to multiply the entire equation by 6.

Explanation:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to find a common denominator for both fractions. The common denominator for 2 and 3 is 6. Therefore, we need to multiply the entire equation by 6 to eliminate the fractions.

Multiplying the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3)

Simplifying further, we get: 3x + 2x = 50

Combining like terms, we have: 5x = 50

Finally, dividing both sides of the equation by 5 gives us:  x = 10

Final answer:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, one must multiply each term by 6, which is the least common multiple of the denominators 2 and 3, making option D correct.

Explanation:

The equation x/2 + x/3 = 25/3 should be multiplied by a number that is a common multiple of the denominators 2 and 3 to eliminate the fractions. To find the least common multiple (LCM) of 2 and 3, we can list out the multiples of these numbers (2,4,6,8,... for 2 and 3,6,9,12,... for 3) and identify the smallest multiple they have in common, which is 6. Therefore, multiplying the entire equation by 6 will eliminate the fractions and give us an equation with whole numbers.

Multiplying each term of the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3). Simplifying each term results in: 3x + 2x = 50 which is an equation without fractions.

The correct answer to the question is D. 6.

11(.25)= 2.75

Cryus should order 3 pizzas.

Answer:

x = 1 11/15

Step-by-step explanation:

Using ratios of similar triangles

3            5.2

-------- = ----------

4            (5.2 + x)

Using cross products

3 * (5.2 + x) = 5.2 * 4

Distribute

15.6 + 3x = 20.8

Subtract 15.6 from each side

15.6-15.6 + 3x = 20.8 -15.6

3x =5.2

Divide each side by 3

3x/3 = 5.2/3

x = 5.2/3

x=52/30

x = 26/15

x = 1 11/15

w - width

2w - length (l)

30 cm - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 30    divide both sides by 6

w = 5 cm

2w = 2(5) = 10

l = 10 cm

The area of a rectangle: A = lw.

Substitute:

A = (5)(10) = 50

Answer:

Hourly labor rate = $14.84

Step-by-step explanation:

Total cost of job = $147.51

Price of parts = $32.50

Labor cost + overhead = Total cost - parts = 147.51 - 32.5

=115.01

Overhead rate = 55%

Labor cost = 115.01/(1+55%) = 115.01/1.55

=74.2

Duration of job = 5 hours

Hourly labor rate = 74.2/5

= $14.84

Answer:

$14.84

Step-by-step explanation:

Total cost of job = $147.51=labor+overhead+parts

Price of parts = $32.50

labor+overhead =147.51-32.5=115.01

Overhead rate = 55%

labor+0.55labor= 115.01

labor=115.01/(1.55)=74.2

Duration of job = 5 hours

hourly labor=74.2/5=$14.84

Answer:

Option a. Greece.

Step-by-step explanation:

According to the table listing average daily expenses for a tourist by country based on high and medium categories,

Brazil has a range from = $12.25 to $18.33

Greece has a range from = $9.48 to $16.55

To find out the difference in range, first we get range of both the countries.

by subtracting lowest from highest

Brazil = $18.33 - $12.25 = 6.08

Greece = $16.55 - $9.48 = 7.07

= 7.07 > 6.08

Therefore, Greece has the larger difference between categories.

Option a. Greece is the correct answer.

Answer:

13,000 meters.

Step-by-step explanation:

We have been given that Lisa went on a 52 km hike. She divided the distance traveled evenly over 4 days.

Let us convert our given distance in meters.

1 km = 1,000 meters.

52 km= 52*1,000 meters = 52,000 meters.

Let us divide total distance traveled by total number of days to find the distance traveled per day.

[tex]\text{Lisa walked each day}=\frac{52000\text{ meters}}{\text{ 4 days}}[/tex]

[tex]\text{Lisa walked each day}=13,000\frac{\text{ meters}}{\text{ day}}[/tex]

Therefore, Lisa walked 13,000 meters each day.

Lisa hiked 52 km in 4 days, equaling to 13 km per day. However, this must be converted to meters, so Lisa hiked 13,000 meters each day.

This problem is an exercise in unit conversion and division. Since Lisa divided the total distance of 52 kilometers evenly over 4 days, she hiked 13 kilometers each day (52 km / 4 = 13 km/day). However, the question asks for the answer in meters, not kilometers. Therefore, we must convert kilometers to meters. We know that 1 kilometer is equivalent to 1000 meters, so Lisa hiked 13,000 meters each day (13 km * 1000 = 13,000 m/day).

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Answer:

32 miles.

Step-by-step explanation:  

We have been given that Elton hiked 16 miles each day on a 12 day hiking trip.

So, the number of miles hiked by Elton in 12 days will be: [tex]16\times 12=192[/tex] miles.

Lola hiked 14 miles each day on her 16 day hiking trip.

So, the number of miles hiked by Lola in 16 days will be: [tex]14\times 16=224[/tex] miles.  

Let us subtract number of miles hiked by Elton from Number of miles hiked by Lola.

[tex]\text{Number of miles that Lola hiked more than Elton}=224-192[/tex]

[tex]\text{Number of miles that Lola hiked more than Elton}=32[/tex]

Therefore, Lola hiked 32 miles more than Elton in all.  

Answer:

D.

Step-by-step explanation:

Add the x values and divide by the amount of x's and same with the y's

Answer:

-5; -40; -640

Step-by-step explanation:

Answer:

option A  and E

Step-by-step explanation:

Arithmetic sequence converge,  only  in the case only when r=0

otherwise , arithmetic sequence goes increasing or decreasing at a constant rate.

So we ignore second and fourth option

If |r|<1 then geometric sequence converge

if |r|>1 then geometric sequence diverge

In option A, r= 1/5  that is less than 1  so it converge

In option C, r= -2 , |r| > 1 so geometric sequence diverge

In option E, r= 2/3 that is less than 1  so it  converges

Answer is option A  and E

Answer:

25,893

Step-by-step explanation:

2.740 x 9.45=25,893

Let the number = X

You have X^8 / X^5

When dividing two numbers with powers, Simplify the expression by subtracting the powers.

8-5=3

so X^8 / X^5 becomes x^3

Now you have x^3 = 64

To find x take the cubic root of 64:

X = ∛64

X = 4

The number is 4

Answer: Congruency criteria used by Ross to prove the opposite sides are congruent is B) ASA congruence postulate

Answer:

The answer would be B

2.5x = 45

(x) would be the number of dolls, multiplied by how much each doll costs ($2.50) and the product would be how much she has to spend. Hope this helps!

To find the width of a rectangle when given the area and length, divide the area by the length:

Width = 59,400 / 330 = 180 feet

Where C = Cost and P = People

C = 2(5p)

In the context of Tia and her five friends:

C = 2(5*6) = 2(30) = 60

C = 60

The cost for Tia and her five friends to be admitted to ice skate and eat is 60$, and the equation to calculate this is C = 2(5p).

The 95% confidence interval for the difference between the mean salaries of all women and men at the company is (−3570.8,−1533.2), which is option C.

Identify the relevant parameters:

Sample size for women (n_w) = 97

Mean salary for women (μ_w) = $45,902

Standard deviation for women (σ_w) = $3865

Sample size for men (n_m) = 75

Mean salary for men (μ_m) = $48,454

Standard deviation for men (σ_m) = $6677

Confidence level = 95%

Calculate the pooled standard error (s_p):

s_p = √[(n_w * σ_w^2 + n_m * σ_m^2) / (n_w + n_m - 2)]

s_p = √[ (97 * 3865^2 + 75 * 6677^2) / (97 + 75 - 2)]

s_p ≈ $4973.49

Calculate the margin of error (z):

Since the sample size is large for both groups (n_w > 30 and n_m > 30), we can use the standard normal distribution (z-score) with a confidence level of 95%.

z = 1.96 (for 95% confidence level)

Calculate the confidence interval:

Lower bound = (μ_w - μ_m) - z * s_p

Lower bound = ($45,902 - $48,454) - 1.96 * $4973.49

Lower bound ≈ -$3570.80

Upper bound = (μ_w - μ_m) + z * s_p

Upper bound = ($45,902 - $48,454) + 1.96 * $4973.49

Upper bound ≈ -$1533.20

Therefore, the 95% confidence interval for the difference between the mean salaries of all women and men at the company is (-$3570.80, -$1533.20), which confirms your answer of option C.

Answer:

$8.82 is the amount of sales tax

Step-by-step explanation:

$90 x .40 = $36.00

$90 + $36 = $126

$134.82 - $126 = $8.82 in taxes

Answer:

40

Step-by-step explanation:

The data is

21,24,25,28,29,35,37,43,44

To find the third quartile we have to arrange the data in increasing order

so the data in increasing order is

21,24,25,28,29,35,37,43,44

total number of values = 9

Median value = (n + 1 )/ 2

                       =(9+1)/2

                       =5th value

so the median is  29

Lower half of the data is the values before the median and upper half of the data is values after the median

so lower half = {21,24,25,28}

Upper half = {35,37,43,44}

so to find the third quartile we will use the upper half of the values

Third quartile means that the median of the values of upper half of the data

As the total No of value in upper half is 4 which is an even no

we will take the middle values of the upper half and take their mean

so

Third Quartile = [tex]\frac{37+43}{2}[/tex]

                        =[tex]\frac{80}{2}[/tex]

                        =40

so the value of third quartile is 40

Final answer:

The third quartile (Q3) of the data set is 40, calculated by finding the average of the two middle numbers of the upper half of the data after excluding the median.

Explanation:

To find the third quartile of a data set, which is also referred to as Q3 or the 75th percentile, one must identify the median of the upper half of the data. For the provided data set (21, 24, 25, 28, 29, 35, 37, 43, 44), with nine values, the median is 29, which is the fifth value. To calculate Q3, we take the upper half of the data set which does not include the median itself. The upper half includes (35, 37, 43, 44), and the median of this half is the third quartile. Since we have an even number of data points in the upper half, we must find the average of the two middle numbers, 37 and 43, which is (37+43)/2 or 40. Therefore, the third quartile of the provided data set is 40.

Answer:

Step-by-step explanation:

a) When will the height be 307 feet?

h = − 16t^2 + 171t + 17

307 = − 16t^2 + 171t + 17

Solving the quadratic equation by the general formula (find the plot attached). It reaches 307' twice as it is a parabolic shot.

t=2.1141s

t=8,5734s

b) When will the object reach the ground?

h = − 16t^2 + 171t + 17

0 = − 16t^2 + 171t + 17

t=-0.0985s (not real as there exists no negative time)

t=10.786s

The object will be at a height of 307 feet approximately 9.54 seconds after it was thrown. The object will reach the ground approximately 0.21 seconds after it was thrown.

To find when the height will be 307 feet, you can set the equation for the height h to 307 and solve for t:

h = -16t² + 171t + 17

307 = -16t² + 171t + 17

Now, let's rearrange the equation and set it equal to zero:

-16t² + 171t + 17 - 307 = 0

Combine like terms:

-16t² + 171t - 290 = 0

Now, you can solve this quadratic equation for t. You can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

In this case, a = -16, b = 171, and c = -290. Plug these values into the quadratic formula:

t = (-171 ± √(171² - 4 * (-16) * (-290))) / (2 * (-16))

Now, calculate the values for t:

t₁ = (-171 + √(171² - 4 * (-16) * (-290))) / (2 * (-16))

t₂ = (-171 - √(171² - 4 * (-16) * (-290))) / (2 * (-16))

Calculate t₁ and t₂ separately:

t₁ ≈ 9.54 seconds

t₂ ≈ -9.69 seconds

Since time cannot be negative in this context, we discard the negative solution. Therefore, the object will be at a height of 307 feet approximately 9.54 seconds after it was thrown.

To find when the object will reach the ground, you can set h equal to 0 and solve for t:

h = -16t² + 171t + 17

0 = -16t² + 171t + 17

Rearrange the equation:

-16t² + 171t + 17 = 0

Now, solve for t using the quadratic formula as we did before:

t = (-171 ± √(171² - 4 * (-16) * 17)) / (2 * (-16))

Calculate t₁ and t₂:

t₁ ≈ 0.21 seconds

t₂ ≈ 10.30 seconds

Again, you discard the negative solution. So, the object will reach the ground approximately 0.21 seconds after it was thrown.

Learn more about equation here

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Answer:

2.4 hours Electrician works.

Step-by-step explanation:

Let us assume that the number of hours  Electrician works be x.

As given

An Electrician charges $30 for a service call plus $75 per hour of service.

If Electrician  charged $210.

Than the equation becomes

30 + 75x = 210

75x = 210 - 30

75x = 180

[tex]x =\frac{180}{75}[/tex]

x =2.4 hours

Therefore 2.4 hours Electrician works.

Answer:

Slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Slope of a line : For any two point [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

the formula of slope is given by:

Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the points ( -4, 7) and (0, 8)

then, by using slope formula;

[tex]m = \frac{8-7}{0-(-4)} = \frac{1}{0+4} = \frac{1}{4}[/tex]

Therefore, the slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]

Answer:

1 / 4

Step-by-step explanation:

We are to find the slope of a line which passes through the two given points: (–4, 7) and (0, 8).

We know the formula of the slope (m):

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

So putting in the values of the coordinates of the given points in the formula to get:

Slope = [tex]\frac{8-7}{0--4} = \frac{1}{4}[/tex]

Therefore, the slope slope of a line which passes through the two given points: (–4, 7) and (0, 8) is 1 / 4.

Answer:

Step-by-step explanation:

Given triangle WXY and <1 is an exterior angle.

We need to prove <1 is greater than <2.

First statement is:

Triangle WXY and <1 is an exterior angle.

Reason : Given

Note: An exterior angle of a triangle is the sum of two angles side the triangle those don't makes the linear pair with exterior angle.

We can see that <2 and < 3 are the angles of triangle those are not making a linear pair.

Therefore, <1 = <2+< 3.

So, the second statement should be first option <1 = <2+< 3.

Hi there! :)

Answer:

7/25 is equivalent to 0.28

Step-by-step explanation:

In order to go from a fraction to a decimal, you need to divide the numerator (top number) by the denominator (bottom number):

7/25 = 7 ÷ 25

7 ÷ 25 = 0.28

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:0.28

Step-by-step explanation:

so you divided 7 and 25 and it gives 0.28