In ms. Morales's class the ratio of boys to girls is 3:7. The class sizes at Ms.morales's school range from 22 to 34 students per class. What is the total number of students in Ms. Morales class
The total number of students in Ms. Morales's class is either 20 or 30, depending on the value of x.
Let the ratio of boys to girls in Ms. Morales's class be 3x:7x, where 3x represents the number of boys and 7x represents the number of girls.
The total number of students in the class is equal to the sum of the number of boys and the number of girls, which is 3x + 7x = 10x.
We don't know the value of x, but we do know that the class size is between 22 and 34 students.
Therefore, we can set up an inequality based on the total number of students:
22 ≤ 10x ≤ 34
Dividing all parts of the inequality by 10, we get:
2.2 ≤ x ≤ 3.4
Since x represents a whole number of students, the possible values for x are 3 (if there are 30 students in the class) or 2 (if there are 20 students in the class).
If x = 3, then the total number of students is:
10x = 10(3) = 30
If x = 2, then the total number of students is:
10x = 10(2) = 20
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
select all ratios equivalent to 7:10
Answer: ratio:14:20 work:7*2=14 10*2=20 ratio:21:30 work: 7*3=21 10*3=30 ratio:28:40 work:7*8=28 10*4=40
Step-by-step explanation: Just multiply the number on the left and right side of the ration by the same number to get an equivalent ratio. I gave some examples above. I hoped this helped.
Why did the Roman have to give each number a different letter?
Answer:
Sorry I dont understand your question? Can you make it more clear please?
Step-by-step explanation:
What is the sales tax rate if a $7,594 purchase will have $569.55 of sales tax added to it?
Answer:
0.075
Step-by-step explanation:
Simplify 9-{X -(7+X)}
A. 16
B. -2x +2
C.-2x +16
D. 2x +2
10. A perfect circle measuring 38 feet across was discovered on Brickell Avenue in Miami in 1998. Known as the Miami Circle at Brickell, it is believed to be a structure built by the Tequesta Indians. Pieces of burnt wood were found at the site and carbon- 14 dating was used to determine the age of the site. The wood chips were found to contain 80% of the atmospheric carbon-14. Calculate the age of the wood chips to verify the approximate age of the Tequesta settlement. Show your work.
Using an exponential function, it is found that the Tequesta settlement is 1845 years old.
What is an exponential function?The exponential equation for a decaying amount of a substance is given by:
\(A(t) = A(0)e^{-rt}\)
In which:
A(0) is the initial value.r is the decay rate, as a decimal.Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.
\(A(t) = A(0)e^{-rt}\)
\(0.5A(0) = A(0)e^{-5730r}\)
\(e^{-5730r} = 0.5\)
\(\ln{e^{-5730r}} = \ln{0.5}\)
\(5730r = -\ln{0.5}\)
\(r = -\frac{\ln{0.5}}{5730}\)
\(r = 0.00012096809\)
Hence, the equation is:
\(A(t) = A(0)e^{-0.00012096809t}\)
The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).
\(A(t) = A(0)e^{-0.00012096809t}\)
\(0.8A(0) = A(0)e^{-0.00012096809t}\)
\(e^{-0.00012096809t} = 0.8\)
\(\ln{e^{-0.00012096809t}} = \ln{0.8}\)
\(-0.00012096809t = \ln{0.8}\)
\(t = -\frac{\ln{0.8}}{0.00012096809}\)
\(t = 1845\)
The Tequesta settlement is 1845 years old.
You can learn more about exponential functions at https://brainly.com/question/25537936
What are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?
Responses
a. relative minimum = −3, relative maximum = −14
b. relative minimum = 1.5, relative maximum = 4.5
c. relative minimum = 1.5, relative maximum = −3
d. relative minimum = −14, relative maximum = −3
Answer:
d
Step-by-step explanation:
As you can tell by the graphs the relative minimum is -14 since that is where the curve ends and -3 is the maximum due to the top curve being at -3
Answer:
d) relative minimum = −14, relative maximum = −3
Step-by-step explanation:
The relative minimum and maximum values are the minimum and maximum y-values of the points in the domain of the function.
From inspection of the given graph, the minimum y-value in the interval [1, 5] is -14 and the maximum y-value in the interval [1, 5] is -3.
Therefore:
Relative minimum = -14Relative maximum = -3How do I find the lower bound and upper bound?
We are 99% confident that the true proportion of employed individuals working at home at least once per week is between 11.8% and 21.8%.
How to solveThe formula for a confidence interval for a proportion is
p ± Z(α/2) * \(\sqrt[(p(1-p))/n],\)
where p is the sample proportion and
n is the sample size.
Given n=250 and 42 individuals working from home, we find
p=42/250
= 0.168.
For a 99% confidence level, Z(α/2) is approximately 2.58.
Plugging in these values, we get 0.168 ± 2.58 * \(\sqrt{[(0.168*(1-0.168))/250]. }\)
This results in an interval (0.118, 0.218).
Therefore, we are 99% confident that the true proportion of employed individuals working at home at least once per week is between 11.8% and 21.8%.
Read more about lower bound here:
https://brainly.com/question/28725724
#SPJ1
(6.2 x 10²) x (3.5 x 10³)
Answer:
\(21.7 x 10^5\)
Step-by-step explanation:
(6.2 x 10²) x (3.5 x 10³)
First, multiply the coefficients: 6.2 x 3.5 = 21.7.
Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.
Therefore, the result is 21.7 x 10^5.
Answer:
3286000
Step-by-step explanation:
Highschool geometry please answer questions 8-10 in the attachment added
I need help on 3 the explanation is above on how to do it. NOT A TEST
64 people were surveyed and 16 of them chose Mystery, so the proportion of people who chose Mystery is given by:
\(\frac{16}{64}=\frac{4\times4}{4\times16}=\frac{1}{4}\)Therefore, the answer is option a: 1/4
URGENT PLS RESPOND!!!
Answer:
\(\huge\boxed{d=\sqrt{17}}\)
Step-by-step explanation:
Simply use the fact that the change in x squared + the change in y squared = the distance squared. (The Pythagorean Theorem)
1^2 + 4^2 = d^2
1 + 16 = d^2
17 = d^2
d = √17
Hope it helps :)
Find the differential of the function w=xsin(2yz^4).
The differential of
\(w = x \sin(2yz^4)\)
is
\(\mathrm dw = \dfrac{\partial w}{\partial x}\,\mathrm dx + \dfrac{\partial w}{\partial y}\,\mathrm dy + \dfrac{\partial w}{\partial z}\,\mathrm dz\)
where the partial derivatives are
\(\dfrac{\partial w}{\partial x} = \sin(2yz^4) \\\\ \dfrac{\partial w}{\partial y} = x \cos(2yz^4) \times 2z^4 = 2xz^4 \cos(2yz^4) \\\\ \dfrac{\partial w}{\partial z} = x \cos(2yz^4) \times 8yz^3 = 8xyz^3 \cos(2yz^4)\)
So the differential dw is
\(\mathrm dw = \boxed{\sin(2yz^4)}\,\mathrm dx + \boxed{2xz^4 \cos(2yz^4)}\,\mathrm dy + \boxed{8xyz^3 \cos(2yz^4)}\,\mathrm dz\)
An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sink hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point A on one side of the sink hole and B on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the other ends of the two ropes meet at point C. Then you recreate the same triangle by using the distance from AC and BC and creating new segments CE and CD. The distance DE is 52.2 ft.
a. What type of triangles have you created?
b. How do you know the triangles are congruent?
c. How far across is the sink hole?
d. What is the perimeter of the triangle ABC?
A) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
Read more about Congruent Triangles at: https://brainly.com/question/1675117
#SPJ1
Answer:
Step-by-step expA) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?
A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
lanation:
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 130 to 190 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.65 cm, y= 81.36 kg, r= 0.309, P-value= 0,002, and y= 106+1.15x. Find the best predicted value of y (weight) given an adult male who is 156 cm tall. Use a 0.10 significance level.
The best predicted weight of a person that is 156 cm is 285.4kg
We have the regression equation asy= 106+1.15
When the adult male is 156 cm tall the weight of this person would be calculated as:
y= 106+1.15*156
y = 106 + 179.4
y = 285.4
Hence we can arrive at the conclusion that the best predicted weight of a person that is 156 cm is 285.4kg
Read more on regression equation here:
https://brainly.com/question/26843436
#SPJ1
\(3\sqrt[3]{x^{2} } -2=7\)
solve for X
Answer:
14
Step-by-step explanation:
Please help me this is hard
30 POINTS PLEASE help
Answer:
m= -1/7
b=2
Step-by-step explanation:
Mystery Number:
I round to 375,400 when
rounded to the nearest hundred
have an odd hundreds digit,
tens digit, and ones digit
My tens and ones digits are
the same and both less than 7
What number am I?
Answer:
Step-by-step explanation:
375355
A fence with 2 gates in it surrounds a lion enclosure.
Each gate is 4 m wide.
an image
What is the length of the fence around the enclosure not including the gates?
The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.
Let's assume the length of the rectangle is 'l' and the width is 'w'.
From the given data, we know that each gate is 4 m wide.
Therefore, the width of the rectangle is:
Width = w + (4 m + 4 m) = w + 8 m
The perimeter of the rectangle is:
P = 2l + 2(w + 8 m) = 2l + 2w + 16 m
Now, we need to subtract the combined length of the two gates from the perimeter:
P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m
So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
For such more questions on length
https://brainly.com/question/28108430
#SPJ8
The base of a solid is bounded by y=x,y=0, and x=1. Find the volume of the solid for each of the following cross sections (taken perpendicular to the y-axis): (a) squares, (b) semicircles, (c) equilateral triangles, and (d) semi ellipses whose heights are twice the lengths of their bases.
To find the volume of the solid, you need to calculate the area of each cross-section and then multiply that by the thickness of the section (which is the distance along the y-axis).
(a) Squares: The cross-sections are squares with sides of length y. The area of a square is side^2, so the area of each square is y^2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the square cross-sections is y^2 * y
(b) Semicircles: The cross-sections are semicircles with radii of length y. The area of a semicircle is (pi * r^2) / 2 , so the area of each semicircle is (pi * y^2) / 2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semicircular cross-sections is (pi * y^2) / 2 * y
(c) Equilateral triangles: The cross-sections are equilateral triangles with side length of y. The area of an equilateral triangle is (s^2 * √3)/4. so the area of each equilateral triangle is (y^2 * √3) / 4. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the equilateral triangle cross-sections is (y^2 * √3) / 4 * y
(d) Semi-ellipses: The cross-sections are semi-ellipses whose heights are twice the lengths of their bases. The area of a semi-ellipse is πab/2, where a and b are the lengths of the semi-major and semi-minor axes respectively. Therefore the area of each semi-ellipse will be (πy^2)/2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semi-ellipse cross-sections is (πy^3)/2
It is important to note that this is a theoretical volume calculation, as the shape of the solid does not have a closed form representation by these functions, but rather, these are an approximation.
Also, for any of these volumes to be meaningful, we have to integrate over the range of the variable y, since it is bounded by the equations y=x, y=0 and x=1, the variable y is limited.
To know more about volume of the solid refer to:
brainly.com/question/21036176
#SPJ4
A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:
Salary Education
40 4
73 1
99 7
57 1
83 8
76 4
109 6
49 0
31 4
32 4
91 2
40 4
65 6
71 2
166 5
61 0
88 1
59 4
132 9
25 0
a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 3 decimal places.)
Salaryˆ= ? + ? Education
b. Interpret the coefficient for Education.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,223.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,223.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.
c. What is the predicted salary for an individual who completed 5 years of higher education? (Round answer to the nearest whole number.)
Salaryˆ $
The linear regression equation between educational attainment (in years of higher education) and annual salary (in $1,000s) be
Salary = 84 - 11×Education
Given, a social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals.
we have to find the sample regression equation for the given model
Salary = β0 + β1Education
On using the different values of salary and education, we get
for salary = 40 and education = 4
40 = β0 + 4β1
for salary = 73 and education = 1
73 = β0 + β1
On subtracting both the equations, we get
33 = -3β1
β1 = -11
On substituting the value of β1, we get
40 = β0 + 4(-11)
β0 = 40 + 44
β0 = 84
So, the regression equation be
Salary = 84 - 11×Education
Hence, the regression equation be
Salary = 84 - 11×Education
Learn more about Linear Regression Equation here https://brainly.com/question/25987747
#SPJ4
Val's whole-house central air conditioner uses 2,500 watts when running. Val runs the AC 5 hours per summer day. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Quantity of electricity used in kilowatts is;
1000 watts = 1 kilowatts
2,500 watts = 2.5 kilowatts
Given that Number of hours Val runs AC per day = 5 hours
Number of days = 30 days
Cost of electricity = $0.18 kilowatts per hour
The Cost of Val’s AC to run for a summer month of 30 days can be calculated as;
= Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity
= 2.5 × 5 × 30 × 0.18
= $67.5
The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.
Learn more about cost:
brainly.com/question/2021001
#SPJ1
is a two digit number always less than a three digit number
Option C is correct. Whether a two-digit number is always less than a three-digit number depends on the first digit in the number.
A number can be a combination of a positive and negative integer. For example,
23 is a 2 positive digits number -231 is a 3 digits number (containing a negative and positive integer)We can see from the numbers that 23 (a two digits number ) is greater than -230 (a 3 digits number) which falsifies the claim that a two-digit number is always less than a three-digit number.
The veracity of the claim all depends on the first digits of the number (whether it is a positive or negative integer)
Learn more here: https://brainly.com/question/4233434
Find the value of the length x rounded to 1 DP.
7m
39°
The diagram is not drawn accurately.
55%
x
The solution is, s = 273
What is arc length?Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length.
here, we have,
r=7m
theta = 39°
we know, s= r*theta
i.e. s = 273
hence, The solution is, s = 273.
To learn more on arc length of circle click:
brainly.com/question/22964077
#SPJ9
4x=3x+10 transversal
Answer:
x=10.
Step-by-step explanation:
4x = 3x + 10
4x - 3x = 10
x = 10
0 is an angle in a right-angled triangle. tan 0 = 23/52 What is the value of 0? Give your answer in degrees to 1 d.p.
The value of the angle θ is approximately 24.2 degrees to 1 decimal place.
In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Given that tan θ = 23/52, we can find the value of the angle θ.
To find the value of θ, we can use the inverse tangent or arctan function. Taking the inverse tangent of both sides of the equation, we have:
θ = arctan(23/52)
Using a calculator or trigonometric tables, we can evaluate the inverse tangent of 23/52. The result is approximately 24.2 degrees.
Note that in the context of a right-angled triangle, the tangent function is defined for acute angles (less than 90 degrees). Since 0 degrees is the smallest possible angle, it is considered an acute angle in this case.
For more such questions on angle
https://brainly.com/question/31615777
#SPJ8
Tamanika received a raise in her hourly pay from 18.00 to $22.50 find the percent Change
Answer:
40.5
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the side length of the base is
10.6
in
10.6 in and the height of the pyramid is
12.3
in
12.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
V = 460.68
Step-by-step explanation:
V=(lwh)/3
Graph the data in the table