The amount of money he earns in 6 weeks is equal to $1512.
Given the following data:
Salary = $9 per hourNumber of hours worked = 28 hours each week.To find the amount of money he earns in 6 weeks:
First of all, we would determine the amount of money he earns each week:
[tex]Weekly\;salary = Salary \times Number \;of \;hours \;worked\\\\Weekly\;salary =9\times 28[/tex]
Weekly salary = $252
In 6 weeks:
Total salary = [tex]252\times6[/tex]
Total salary = $1512
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Joe measured 1/2 cup of water. Mary measured 3/4 cup, and Ron measured 3/8 cup. How can the least amount of water be completed to the greatest amount
Answer:
3/8, 1/2, 3/4.
Step-by-step explanation:
Now I believe this is asking to set the fractions from least to greatest, but ignore this if im wrong. If so, the answer would be 3/8, 1/2, 3/4. 3/8 is less than 4/8, which is the halfway point for the 8ths, 1/2 is half of a whole, and 3/4 is more than 2/4, the half for 4ths.
8 solid iron sphare with radius 'a cm' each are melted to form a sphare with radius 'b cm'. find the ratio of a:b
8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm' then the ratio of a:b is 1 : 2
Solution:
Given that 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'
Need to find the ratio of a:b
As 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'.
For sake of simplicity, let volume of 1 sphere of radius a cm is represented by [tex]V_a[/tex] and volume of 1 sphere of radius b cm is represented by [tex]V_b[/tex]
So volume of 8 solid iron sphere with radius 'a cm' = volume of 1 solid iron sphere with radius 'b cm'
[tex]=>8 \times} \mathrm{V}_{\mathrm{a}}=\mathrm{V}_{\mathrm{b}}[/tex]
[tex]\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{b}}}=\frac{1}{8}[/tex] ---- eqn 1
[tex]\text {Let's calculate } {V}_{a} \text { and } V_{b}[/tex]
Formula for volume of sphere is as follows:
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Where r is radius of the sphere
Substituting r = a cm in the formula of volume of sphere we get
[tex]V_{a}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi a^{3}[/tex]
Substituting r = b cm in the formula of volume of sphere we get
[tex]V_{b}=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi b^{3}[/tex]
[tex]\text { Substituting value of } V_{a} \text { and } V_{b} \text { in equation }(1) \text { we get }[/tex]
[tex]\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}[/tex]
[tex]\begin{array}{l}{=>\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}} \\\\ {=>\left(\frac{a}{b}\right)^{3}=\left(\frac{1}{2}\right)^{3}} \\\\ {=>\frac{a}{b}=\frac{1}{2}}\end{array}[/tex]
a : b = 1 : 2
Hence the ratio of a:b is 1 : 2
Final answer:
The ratio of the radius 'a' of the original smaller spheres to the radius 'b' of the new larger sphere formed by melting the 8 smaller spheres together is 1:2, obtained by equating the volumes and simplifying.
Explanation:
The question pertains to using the concept of volumes of spheres in Mathematics to find the ratio of radii of the original smaller spheres to the new larger sphere formed by melting them together. Given that there are 8 solid iron spheres each with radius 'a cm', and they are melted to form one single sphere with radius 'b cm', we preserve the volume during the melting process.
We know that the volume of a sphere is calculated using the formula [tex]V=\frac{4}{3}\pi r^{3}[/tex]. When combining the volumes of the 8 smaller spheres into one large sphere, the volumes on both sides must be equal since no material is lost during melting. The equation to find the volume of the large sphere is [tex]V=8(\frac{4}{3}\pi a^{3}) = \frac{4}{3}\pi b^{3}[/tex].
Simplifying this equation, we obtain the cubic ratio of radii a³/b³ = 1/8. Taking the cube root of both sides, the simple ratio of the radii is a/b = ∛[1/8], which simplifies to a/b = 1/2. Therefore, the ratio of the radius of the smaller sphere to the radius of the larger sphere, a:b, is 1:2,
Students were surveyed about their wither break plans.Of the people that stated they were going skiing, 25% did not actually go.How many students actually went skiing?
Answer:
The number of students who actually went for the skiing is 0.75 times the total number of students .
Step-by-step explanation:
Given as :
Students were surveyed about their wither break plans
The percentage of students who did not go for skiing = 25 %
So, The percentage of students who did not go for skiing =100 % - 25 % = 75%
Let The total number of students = x
So, The number of students actually went for the skiing = 75% of the total number of students
I.e The number of students actually went for the skiing = [tex]\frac{75}{100}[/tex]× x
Or, The number of students actually went for the skiing = 0.75× x
∴ The number of students actually went for the skiing = 0.75 x
Hence The number of students who actually went for the skiing is 0.75 times the total number of students . Answer
assume that the height of men are normally distributed with a mean of 70.9 inches and a standard deviation of 2.1 inches if 36 men are randomly selected find the probability that they have the mean height greater than 71.9 inches
Answer:
Your answer would be 33.7619047619
Step-by-step explanation:
47. A medication is supplied in a 400-mg scored tablet. A physician prescribes 200 mg every 6 hours for
14 days. How many tablets will be dispensed for the entire course of therapy?
A. 7
B. 14
C. 28
D. 56
28 tablets will be required for course of therapy.
One tablet is of 400-mg and prescription is for 200 mg for every 6 hours for 14 days. total number of tablets to be find out.
Arithmetic operation are Addition, subtraction, division, and multiply in order to achieve mathematical solution of the statement.
Here, tablet for a day = 200-mg/400-mg x 24 hr/6 hr
= 1/2 x 4
= 2 Tablets a day
Now, for number of tablets for 14 days course,
= 14 x 2
= 28 Tables in 14 days
Thus, 28 tablets will be required for course of therapy.
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What is the sum of interior degrees for a 13-gon?
How many degrees in each angle for a regular 13-gon?
What is the sum of interior degrees for a 23-gon?
How many degrees in each angle for a regular 23-gon?
What is the sum of interior angles for a triangle?
What is the sum of interior angles for a quadrilateral?
What is one difference, and one similarity between a Square and a Rhombus?
Answer:
1980°
152.3°
3780°
164.35°
180°
360°
Step-by-step explanation:
The sum of all the interior angles of a polygon is given by (n - 2)180° where n is the number of sides.
So, the sum of all interior angles of a 13-gon is (13 - 2) 180° = 1980° (Answer)
As the 13-gon is regular, so each angles will be same. Assume each angle is x°.
So, 13x = 1980, ⇒ x = 152.3° (Answer)
Now, the sum of all interior angles for a 23-gon will be (23 - 2) 180° = 3780° (Answer)
Again,as the 23-gon is regular, so each angles will be same. Assume each angle is x°.
So, 23x = 3780, ⇒ x = 164.35° (Answer)
The sum of all the interior angles of a triangle is 180° (Answer)
The sum of all the interior angles of a quadrilateral is 360° (Answer)
The similarity between a square and a rhombus is all the sides of both are same and the difference, between a square and a rhombus is that a square has every angle 90°, but the rhombus has no angle equal to 90°. (Answer)
svetlanas hair is 4 centimeters long her hair grows 1.5 centimeters per month. Svetlana wants her hair to be less than 16 centimeters long.
Answer:
I guess the question is when her hair will be almost 16cm long.
So she needs to grow hair almost 12 cm of hair. Because 16-4=12
To grow 12cm hair she needs 8 months (12/1.5=8)
So Svetlana needs to cut her hair before 8th month.
What is the simple interest for a principal of $650 invested at a rate of 9% for 5 years?
Answer: 292.50 dollars
Work Shown:
P = 650 is the the principal.
r = 0.09 is the interest rate in decimal form.
t = 5 is the number of years.
i = P*r*t
i = 650*0.09*5
i = 292.50 is the simple interest.
Given values:
Principle,
P = $650Rate,
r = 9% or 0.09Time,
t = 5 yearsAs we know,
→ [tex]i = R\times r\times t[/tex]
By substituting the values, we get
[tex]= 650\times 0.09\times 5[/tex]
[tex]= 292.50[/tex]
Thus the response above is right.
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The diagonal length of a rectangular playing field is 76 feet, and its width is 48 feet. How long is the playing field?
The length of playing field is 58.9 feet
Solution:
Given that, the diagonal length of a rectangular playing field is 76 feet,
And its width is 48 feet.
To find: length of playing field
Now, we know that, diagonal, width and length of a rectangle will form an right angle triangle with diagonal as hypotenuse.
So, now, in a right angled triangle we can use pythagorean theorem to find the length
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition, In a right angled triangle ABC we get
[tex]c^2 = a^2 + b^2[/tex]
Where "c" is the length of hypotenuse
"a" is the length of one leg of right angled triangle
"b" is the length of other leg of right angled triangle
[tex]\begin{array}{l}{\text {Then, diagonal = width }^{2}+\text { length }^{2}} \\\\ {76^{2}=48^{2}+\text {length }^{2}} \\\\ {\text {Length }^{2}=76^{2}-48^{2}} \\\\ {\text {Length }^{2}=5776-2304}\end{array}[/tex]
[tex]\begin{array}{l}{\text { Length }^{2}=3472} \\\\ {\text { Length }=\sqrt{3472}} \\\\ {\text { Length }=58.92}\end{array}[/tex]
Hence, the length of the rectangular field is 58.9 feet
Answer:The answer is 3,472
Step-by-step explanation:
I GOT THIS CORRECT TRUST ME!! :)
Which of the following is an example of an expression?
7x - 8y + 11z = 22
11z = 22
7x = 22
7x - 8y + 11z
Answer:
7x-8y+11z
Step-by-step explanation:
Because this is the only one that doesn't have an equal sign. Therefore, this is an example of an expression, not a equation. All of the other answer choices have an equal sign, they're equations.
Evaluate the expression when b=5 and x=-3
Answer:
-33
Step-by-step explanation:
x-6b when b=5 and x=-3
-3-6(5)=-3-30=-33
Find out
[tex] {5}^{10} + {8}^{3} [/tex]
Answer:
[tex]5^{10}+8^3[/tex]
[tex]5^{10}=9765625[/tex]
[tex]8^3=512[/tex]
[tex]=9765625+512[/tex]
[tex]=9766137[/tex]
OAmalOHopeO
on a farm there are 3 sheep for every 1 horse. if y = the number of sheep, and X = the number of horses, which graph models the relationship?
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x ----> the number of horses
y ---> the number of sheep
In this problem the relationship between the variables, x, and y, represent a proportional variation.
Remember that, if the linear equation represent a proportional variation then it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
we have
For x=1, y=3
Find the value of the constant of proportionality k
[tex]k=\frac{3}{1}=3\ \frac{sheeps}{horse}[/tex]
substitute
[tex]y=3x[/tex]
using a graph tool
The graph in the attached figure
There are 11 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible
There are 165 different subcommittees possible.
Explanation:To calculate the number of different subcommittees possible, we can use the combination formula. The number of different subcommittees is equal to the number of ways to choose 3 members out of 11. This can be calculated using the formula C(n, r) = n! / (r! (n - r)!), where n is the total number of members and r is the number of members in the subcommittee.
Plugging in the values, we have C(11, 3) = 11! / (3! (11 - 3)!) = 165. Therefore, there are 165 different subcommittees possible.
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5(1+4r)- 8(4-r) simplify
Answer: =28r−27
Step-by-step explanation:
Answer:
= 25r - 32-r
Step-by-step explanation:
5(1+4r)-8(4-r)
= 5 x 5r - 32-r
= 25r - 32-r
If r was 2, (example),
= 25 x 2 - 32 - 2
= 50 - 30
= 20
please help wit all questions! leave work below! if you do this , it will give you 40 points!!
Answer:
13. ft per minute is 150. ft per hour is 9,000.
work:
300÷ 2 = 150150 times 60 min.14. x ÷ y = feet per minute.
it is this because the time divided by the depth will equal the time that it took.
15. it would be more reasonable to use feet by minute, because of the accuracy of the answers. with measuring it using feet per hour, your answers will be less precise.
16. the distance will double because the proportional relationship says that the distance is 3 km away if thunder is 9 secs apart from lightning.
will answer next question later
If the variance for the data set is 104.4, what is the standard deviation?
Answer: 10.22
Step-by-step explanation:
Standard Deviation = square root of variance 104.44 = 10.22
Final answer:
To find the standard deviation from the variance of 104.4, you take the square root of the variance, resulting in a standard deviation of approximately 10.22.
Explanation:
If the variance for a data set is 104.4, to find the standard deviation, you take the square root of the variance. The formula to calculate the standard deviation (s) from the variance (σ²) is:
s = √σ²
Applying this formula, the standard deviation would be s = √104.4. Using a calculator, you would get:
s ≈ 10.22
Thus, the standard deviation for the data set with a variance of 104.4 is approximately 10.22.
Stephanie is packing her bags for her vacation. She has 7 unique books, but only
3 fit in her bag. How many different groups of
3 books can she take?
Answer:
35
Step-by-step explanation:
Need help with this problem.
Answer:
18
Step-by-step explanation:
To find this we must divide 45 by 20 which gives the answer of 2.25. As we know this we now must multiply that by 8 resulting in to 18.
Therefore the answer is 18
which of the following is equivalent to the expression 5^3*5^-5 there are 3 /A-5^-2, B- 1 /5^2 C- 5^2, D- 1 5^-2, E- 1 /25
Answer:
e-1/25
Step-by-step explanation:
During a Grand Prix car race, the tyres on a car are reduced in mass by 3%. If their mass is 388 kg at the end of the race, what was their mass at the start?
Answer:
Their mass at the start was 400 kg.
Step-by-step explanation:
Given:
The tyres on a car during a grand prix race are reduced in mass by 3%. Their mass is 388 kg at the end of the race.
Now, to find the mass at the start.
Let the mass at the start be [tex]x[/tex].
According to question:
[tex]x - 3 \%ofx= 388[/tex]
⇒[tex]x-\frac{3}{100}\times x = 388[/tex]
⇒[tex]x-0.03x =388[/tex]
⇒[tex]0.97x=388[/tex]
Dividing both sides by 0.97 we get:
⇒[tex]x=400[/tex]
Therefore, their mass at the start was 400 kg.
To find the original mass of the tyres before the 3% decrease, we make a simple percentage calculation. By setting up the equation 97/100 * x = 388, we find that the original mass of the tyres was 400 kg.
Explanation:The question posted is a mathematics problem related to understanding percentages and its application to real-life situations such as a Grand Prix race.
Given that the tyres at the end of the race have a mass of 388 kg, which is 97% of their original mass (since they lost 3%), we can find their original mass by setting up a simple percentage equation. We denote the original mass as 'x' and set up the equation: 97/100 * x = 388. To solve for 'x', we divide both sides of the equation by 97/100, which is equivalent to multiplying by its reciprocal, 100/97.
The solution to the problem is then calculated as following: x = 388 * (100/97) = 400 kg.
Hence, the original mass of the tyres was 400 kg.
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What is the equation of the line that passes through the point (-4, 8) and has a slope of zero
Answer:
here you go If the slope is undefined, it means that it is a vertical line. This means that it passes through all points in the y direction. Since the x value is -4, and the line is vertical, that's the only x value on that line. So you just say the equation of the line is x=-4
Step-by-step explanation:
Answer:
y=8
Step-by-step explanation:
y-y1=m(x-x1)
m=0
y-8=0(x-(-4))
y-8=0(x+4)
y-8=0
y=0+8
y=8
A rug is shaped like a parallelogram with a base of 41⁄2 ft. and a height of 2 1⁄4 ft. What is the area of the rug? Draw and label the dimensions of the shape then find the area.
Answer:
46.125 square feet or [tex]46\dfrac{1}{8}[/tex] sq. feet.
Step-by-step explanation:
The rug is shaped like a parallelogram with a base of [tex]\frac{41}{2} = 20.5[/tex] feet. and a height of [tex]2\dfrac{1}{4} = 2.25[/tex] feet.
Now, the area of a parallelogram is given by the product of one side as the base and the perpendicular distance of that side from the opposite parallel side as height.
Now, the area of the given parallelogram is (20.5 × 2.25) = 46.125 square feet. (Answer)
a cat owner paid the vet a fee of$269.50 for a years worth of visits. he made 14 visits that year. what was the average per cost?
Answer:
The average per cost is $19.25.
Step-by-step explanation:
Given:
The fee paid by cat owner = $269.50. Total visits he made that year 14.
Now, to find the average per cost.
So, to get the average per cost we divide the total fee by total visits:
Average per cost = Total fee ÷ Total visits
= [tex]269.50\div 14[/tex]
= [tex]19.25[/tex]
Therefore, average per cost is $19.25.
Answer:
The Average cost of per visit to the vet = $ 19.25
Step-by-step explanation:
Here, the total visits to the vet in a year = 14
Also, the total amount paid to the vet in a year = $269.50
Now, Let us assume the average cost per vet visit = m
So,[tex]\textrm{Average cost of per visit} = \frac{\textrm{Total amount paid in n visits}}{\textrm{ n visits}}\\ \implies m = \frac{269.50}{14} = 19.25[/tex]
or, m = $ 19.25
Hence, the Average cost of per visit to the vet = $ 19.25
If the average football player weighs 250 pound, how much would the starting defense weigh? (There are 11 players on each team on the field)
Answer:
2750
Step-by-step explanation:
As there are 11 players on the field, each averaging 250 pounds, this means that we can add 250 11 times, 1 for each player. Another way to say this would be to multiply 250 and 11, as we are adding 250 11 times. Our answer is then 250*11 = 2750.
What is the third quartile of this data set? 14, 18, 20, 21, 25, 32, 38, 42, 48
Answer: the answer is 40
Which term best describes the relationship between time and number of labels printed?
A. double
B. decreasing
C. proportional
Answer:
C proportional
Step-by-step explanation:
The answer is c because
proportional means equal
and as u can see in the photo you have represented a proportional relationship because ther line is going in and equal line across the axis and it is increasing at a proportional rate!
and there you go!
find values of x y and z
Answer:
Well, we know x has to add up to 180 degrees since a triangle has 180 degrees in it!
63 + 36 = _99__
180 - 99 = 81
81 = x
180 - 81 = 99
99 is z
99 + 13 = 112
180 - 112 = 68
68 is y
Since 13 is an angle measurement. We add to get 180.
68 = y
99 = z
81 = x
In a auditorium, there are 9 rows of seats with 18 seats in each row. There are also 6 rows of seats with 24 in each row. How many seats are there in the auditorium? Estimate first. Then check for reasonableness
Answer:
there are 306 in total
Step-by-step explanation:
Question 5
Find the sum of the following geometric series.
8+1.6+0.32+0.064 + ...
good morning,
Answer:
10×(1-0.2ⁿ)
Step-by-step explanation:
1.6/8=0.2
0.32/1.6=0.2
0.064/0.32=0.2
let S represent the sum of n term then S=8×[(1-0.2ⁿ)/(1-0.2)] = 10×(1-0.2ⁿ).
:)
Final answer:
To find the sum of a geometric series, use the formula for the partial sum by identifying the first term and common ratio.
Explanation:
A geometric series is represented by the formula a + ax + ax² + ax³ + ... with a as the first term and x as the common ratio. The sum of the first N terms of a geometric series can be found using the formula of the partial sum.
In the given series 8+1.6+0.32+0.064+..., the first term a = 8 and the common ratio x = 0.2. To find the sum, you can use the formula for the sum of a geometric series: S = a / (1 - x).
Substitute a = 8, x = 0.2 into the sum formula: S = 8 / (1 - 0.2) = 8 / 0.8 = 10. Therefore, the sum of the given geometric series is 10.