Answer:
6
Step-by-step explanation:
Given I varies inversely with R then the equation relating them is
I = [tex]\frac{k}{R}[/tex] ← k is the constant of variation
To find k use the condition R = 12 when I = 3
k = IR = 3 × 12 = 36
I = [tex]\frac{36}{R}[/tex] ← equation of variation
When I = 6, then
6 = [tex]\frac{36}{R}[/tex], hence
R = [tex]\frac{36}{6}[/tex] = 6
Zinc has a density of 0.258 lb/in³ (pounds per cubic inch).
Darius is making a pyramid out of solid zinc. The pyramid has a square base 6 inches on each side, and a height of 2.5 inches.
How many pounds of zinc does he need?
DO NOT ROUND FINAL ANSWER!!!
Why don’t you round the last answer
For this case, we have that by definition:
ρ = [tex]\frac {M} {V}[/tex]
Where:
ro: Density
M: Mass
V: Volume
We find the volume of the pyramid:
[tex]V = \frac {1} {3} * l ^ 2 * h[/tex]
Where:
[tex]l ^ 2[/tex]: Represents the area of the base of the square pyramid
h: Represents the height
So:
[tex]V = \frac {1} {3} * (6) ^ 2 * 2.5\\V = \frac {1} {3} * 36 * 2.5\\V = 30 \ in ^ 3[/tex]
We have to:
M = ρ* V
[tex]M = 0.258 \frac {lb} {in ^ 3} * 30 \ in ^ 3\\M = 7.74 \ lb[/tex]
So, you need 7.74 pounds of zinc
Answer:
7.74 pounds
The temperature in Oslo was −20∘C at midday. At 4 pm, the temperature rose 3∘C, and then dropped 8∘C at 8 pm. Anyone Help me out? Because im not sure with with the rising by 3 degrees C part, because I think that it is - 20 + 3 which = -23 or -17 im not sure please help me out
You are on the right track: - 20 + 3 = - 17 but do not forget about "dropped 8°C"
-20 + 3= -17
You are correct.
At an elementary school, the fourth-grade class is planning a field trip to the science center. The roster shows 113 students who will attend the event. School-district rules specify that there must be one adult chaperone for every 10 students.
Which equations correctly represent this situation, where c is the number of chaperones?
Select all that apply.
10c=113
113=c10
10=c113
c=113(10)
c=11310
Answer:
10c=113
113=c10
Step-by-step explanation:
Either is same. For multiplication, even though you flip it, it is same.
Answer:
10c=113
113=c10
c=113/10
Step-by-step explanation:
What is the slope of the line?
Answer:
7/4
Step-by-step explanation:
up seven, right four
7/4. Go up seven, right 4
what could tara have written as the result from step 2?
Answer: (x-30)^2=4
Step-by-step explanation:
Hamill finds the measure of x to be 90. He justified his work by writing “ all exterior angles of a polygon are found by 360/n. Which of the following statements explain why his answer is incorrect
Answer:
the polygon is not regular and the 360/n formula is only applies to regular polygons
Step-by-step explanation:
Find the solution set for this inequality: -3x -12> 8x+ 21
-3x - 12 > 8x + 21
Step 1: Combine like terms
x's go with x's (-3x and 8x). To do this add 3x to both sides
(-3x + 3x) - 12 > (8x + 3x) + 21
-12 > 11x + 21
Normal numbers go with normal numbers (-12 and 21). To do this subtract 21 to both sides
(-12 - 21) > 11x + (21 - 21)
-33 > 11x
Step 2: Isolate x by dividing 11 to both sides
-33/11 > 11x / 11
-3 > x
Hope this helped!
Answer:
[tex]x\:<\:-3[/tex]
Step-by-step explanation:
The given inequality is:
[tex]-3x-12\:>\:8x+21[/tex]
We group similar terms to obtain:
[tex]-12-21\:>\:8x+3x[/tex]
Combine the similar terms to obtain:
[tex]-33\:>\:11x[/tex]
Divide both sides by 11;
[tex]-3\:>\:x[/tex]
Or
[tex]x\:<\:-3[/tex]
A group of randomly selected members of Mothers' Club were asked how many kids they have. The table below shows the results A group of randomly selected members of Mothers' Club were asked how many kids they have. The table below shows the results of the survey. There are 120120120 members in Mothers' Club. Number of kids Number of mothers 111 999 222 666 3+3+3, plus 555 Based on the data, what is the most reasonable estimate for the number of Mothers' Club members who have fewer than 222 kids?the survey. There are 120120120 members in Mothers' Club. Number of kids Number of mothers 111 999 222 666 3+3+3, plus 555 Based on the data, what is the most reasonable estimate for the number of Mothers' Club members who have fewer than 222 kids?
Answer:
54
Step-by-step explanation:
Estimate=Population size × Sample proportion
population size = 120
sample proportion = (9)/(9+6+5) = 9/20 (check on Cymath as a resource)
estimate = 120 x 9/20 = 54
The estimation will be 54 for the number of mothers.
What is estimation?The estimation is the approximated results of anything it can be the possibility or probability of any event to happen or any number to come.
Estimate=Population size × Sample proportion
population size = 120
sample proportion = (9)/(9+6+5) = 9/20 (check on Cymath as a resource)
Estimate = 120 x 9/20 = 54
Hence estimation will be 54 for the number of mothers.
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What is the ratio of books to pencils?
Answer:
A. 4/7
Step-by-step explanation:
If Susie has a bag with 9 hairpins, 7 pencils, 2 snacks, and 4 books, the ratio of books to pencils is 4/7 or 4:7.
4 books.
7 pencils.
You could combine the 4 and 7 getting, 4/7 or 4:7
Even though, there are more numbers, the question only asked for the ratio of books to pencils.
How do I find the Circumference?
2* radius* pie
Step-by-step explanation:
first you times 2 by the radius, then you times that answer by 3.14.
hoped this helped a little
The total deposit and rent collected by an apartment manager for one resident are given by the equation t = 350 + 700m, where m is the number of months the resident has lived there. Is this model of the situation linear? If it is, what are the slope and the y-intercept?
A. linear: slope = 350, y-intercept = 700
B. linear: slope = 700, y-intercept = 350
C. linear: slope = 2, y-intercept = 350
D. not linear
A linear equation is an equation in which each term has at max one degree. The correct option is B.
What is a linear equation?A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
The total deposit and rent collected by an apartment manager for one resident are given by the equation t = 350 + 700m, where m is the number of months the resident has lived there. Since the equation is in the form of a linear equation it can be concluded that the model is linear.
Comparing the equation with a linear equation,
t = 350 + 700m
y = C + mx
The slope of the equation is 700, while the y-intercept is 300.
Hence, the correct option is B.
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What number must you add to complete the square x^2+2x=9
Answer:
+ 1
Step-by-step explanation:
Given
x² + 2x = 9
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(1)x + 1² = 9 + 1²
(x + 1)² = 10
Answer:x =(-2-√-32)/-2=1+2i√ 2 = 1.0000-2.8284i
x =(-2+√-32)/-2=1-2i√ 2 = 1.0000+2.8284
Step-by-step explanation:
melissa and angie baked 15 pies for the bake sale on Pi day and were suprised when they sold every piece for $2.25 each. If their ingredients were $15.24 for all pies and each pie was cut into six slices, How much profit did the girls make in the bake sale?
$18.51 would be the correct answer!
Find the value of the combination. 16c14 HELP
Answer:
120
Step-by-step explanation:
We need the formula of combination:
nCr = [tex]\frac{n!}{(n-r)!*r!}[/tex]
Also we need to understand "factorial" notation, which is the "!" mark. For example, 5! means 5 * 4 * 3 * 2 * 1, and
4! would mean 4 * 3 * 2 * 1
Now we can find out 16C14 by plugging it into the formula and doing the steps shown below:
[tex]nCr=\frac{n!}{(n-r)!*r!}\\16C14=\frac{16!}{(16-14)!*14!}\\=\frac{16!}{2!*14!}\\=\frac{16*15*14!}{(2*1)*14!}\\=\frac{16*15}{2}\\=120[/tex]
What is the completely factored form of x^4+8^2-9?
Answer: wads
Step-by-step explanation:wasd
Answer:
Is that equation typed correctly?
For one thing, that second term should (probably) be 8x^2.
Step-by-step explanation:
Determine the equation of the line for the given information: Two points on the line are (0, 4) and (7, 18). Use the points to first determine the slope and y-intercept. Then write the equation of the line
Answer:
y = 2x + 4
slope: 2
y-intercept: (0,4)
Step-by-step explanation:
to find the slope and y-intercept of the two points, we can use the following formula:
y2 - y1/ x2 - x1 = slope
to solve, we plug in the values into the equation
we will treat (0,4) as x1, y1 and (7,18) as x2, y2
y2 - y1 = 18 - 4 = 14
x2 - x1 = 7 - 0 = 7
14/7 is the slope, but we can simplify as 14/7 is equal to 2
so the slope is 2 (can also be said as 2/1)
we can now put the following slope into slope-intercept form (y=mx+b)
y = 2x + b < b is the slope, we so we need to solve for b
looking at our points (0,4) and (7,18), we see that we have the y-intercept, as the y-intercept has the x-coordinate 0, and any y-coordinate. the y-intercept is (0,4)
but if we dont have the y-intercept that easily, we can plug in any coordinate that we are given into the equation and solve for b. for this example, ill use (0,4) to plug into the equation
4 = 2(0) + b
4 = b
the y-intercept is 4
the final equation would be the following:
y = 2x + 4
The equation of the line that passes through two points (0, 4) and (7, 18) is y = 2x + 4.
To determine the equation of the line using the given information, we first need to find the slope and y-intercept. The slope of a line can be calculated using the formula:
slope (m) = (change in y-coordinates) / (change in x-coordinates)
Using the points (0, 4) and (7, 18), we can calculate the slope:
slope (m) = (18 - 4) / (7 - 0) = 14 / 7 = 2
So, the slope of the line is 2.
Next, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can substitute one of the points into the equation and solve for b.
Using the point (0, 4):
4 = 2(0) + b
b = 4
Therefore, the y-intercept (b) is 4.
Finally, we can write the equation of the line:
y = 2x + 4
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a movie theater has 18 rows with 15 seats each how many seats does the theater have
The answer is : 270 seats
Multiply 18*15
18*15
=270
Answer: 270 seats
0.000000057 in scientific notation would be:
Answer:
[tex]\large\boxed{0.000000057=5.7\cdot10^{-8}}[/tex]
Step-by-step explanation:
[tex]\text{Scientific notation:}\\\\a\cdot10^k\\\\\text{where}\ 1\leq a<10\ \text{and}\ k\in\mathbb{Z}\\-------------------------\\\\0\underbrace{.00000005}_{8\rightarrow}7=5.7\cdot10^{-8}[/tex]
If you move the comma several places to the right, the exponent at 10 is negative.
If you move the comma several places to the left, the exponent at 10 is positive.
Solve this system of linear equation. Supérate the x- and y-values with a comma. 2x+4y=-48 4x-9y=57
Answer:
(x,y) = (-6.12,-11.76)
Step-by-step explanation:
2x+4y=-48 => eq(i)
4x-9y=57 => eq(ii)
We need to solve these equations simultaneously to find the values of x and y.
Multiplying eq(i) with 2 and subtracting both equations
4x + 16y = -96
4x - 9y = 57
- + -
__________
25 y = -153
y = -153/25
y = -6.12
Putting value of y in eq(i)
2x + 4(-6.12) = - 48
2x - 24.48 = -48
2x = -48 + 24.48
2x = -23.52
x= -23.52/2
x= -11.76
So, values of x and y are -6.12 and -11.76
(x,y) = (-6.12,-11.76)
The solution to the system of linear equations is [tex]\(x = -6\) and \(y = -9\).[/tex]
Let's solve the system of linear equations:
[tex]1. \(2x + 4y = -48\)\\2. \(4x - 9y = 57\)[/tex]
We can use the substitution or elimination method. I'll use the elimination method here:
Multiply the first equation by 2 to make the coefficients of [tex]\(x\)[/tex]in both equations the same:
[tex]1. \(4x + 8y = -96\)\\2. \(4x - 9y = 57\)[/tex]
Now, subtract the second equation from the first to eliminate [tex]\(x\):[/tex]
[tex]\((4x + 8y) - (4x - 9y) = -96 - 57\)[/tex]
Simplify:
[tex]\(17y = -153\)[/tex]
Now, solve for \(y\):
[tex]\(y = -\frac{153}{17} = -9\)[/tex]
Now that we have \(y\), substitute it back into one of the original equations. I'll use the first equation:
[tex]\(2x + 4(-9) = -48\)[/tex]
Simplify:
[tex]\(2x - 36 = -48\)[/tex]
Add 36 to both sides:
[tex]\(2x = -12\)[/tex]
Divide by 2:
[tex]\(x = -6\)[/tex]
So, the solution to the system of linear equations is [tex]\(x = -6\) and \(y = -9\).[/tex]
what is the area of a sector when theta = 15º and r = 4
Answer:
2.09 sq. units
Step-by-step explanation:
We can simply use the formula for area of a sector of a circle.
Area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]
Where [tex]\theta[/tex] is the angle and r is the radius.
It is given that the angle is 15 and radius is 4. We plug them in and find the area:
[tex]\frac{\theta}{360}*\pi r^2\\=\frac{15}{360}*\pi (4)^2\\=\frac{1}{24}*16\pi\\=2.09[/tex]
Thus area of sector is 2.09 sq. units.
Answer:
2pi/6
Step-by-step explanation:
If you convert the degrees to radians (15 degrees theta) you get:
15/1 * pi/180 --> =15pi/180 then you multiply by the radius --> 15pi/180 *4/1
this gives you 60pi/180 (don't forget to reduce) =2pi/6
(Sorry this is so confusingly written out. I wish I could have just shown you on paper but just remember that all of the "/" mean a fraction! :) )
Among 1501 respondents to a survey, 20% said that there is no solid evidence to support global warming. Use a 0.01 significance level to test the claim that less than 25% of the population believes that there is no solid evidence of global warming. State the final conclusion. A. There is not sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming. B. There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming. C. There is sufficient evidence to support the claim. D. There is sufficient evidence to support the claim that more than 25% of the population believes that there is no solid evidence to support global warming.
Answer:
B. There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.
Step-by-step explanation:
The following information has been availed;
n = 1501
sample proportion = 20% = 0.2
Level of significance = 0.01 = 1%
We are required to test the claim that less than 25% of the population believes that there is no solid evidence of global warming. In mathematical notation this claim can be written as;
p < 0.25, where p is the population proportion. From this information, we can formulate the following set of hypotheses;
H0: p ≥ 0.25
Ha: p < 0.25 (claim). This will be a left-tailed test.
The test statistic for hypothesis on population proportions is z, defined by the formula;
[tex]z=\frac{sampleproportion-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
where p is the population proportion under the null hypothesis, that is p = 0.25.
Using the given information , the test statistic becomes;
[tex]z=\frac{0.2-0.25}{\sqrt{\frac{0.25(1-0.25)}{1501} }}=-4.4736[/tex]
The next step is to compute the p-value in our left-tailed test;
p-value = P(Z < -4.4736) = 0
Our p-value is less than the level of significance and thus we reject the null hypothesis in favor of the alternative hypothesis which is also our claim. The final conclusion is thus;
There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.
Adam calculates his annual commission, y, using the model y = 0.28x, where x represents his total sales for the year. What is the meaning of the x-intercept in the model?
Answer:
The x intercept is where Adam made 0 commission for x number of sales.
Step-by-step explanation:
The x intercept is where the line crosses the x axis. It has a point (a,0) where y=0. In this model y is Adams total commission and x is his total sales. The x intercept is where Adam made 0 commission for x number of sales.
What is the median of 23 2 5 14 25 36 27 42 12 8 7 23 29 28 11 20 31 8 36
Answer:
23
Step-by-step explanation:
The median is the number in the middle of the data once it is organized from least to greatest, so that is what we must do first.
[tex]2,5,7,8,8,11,12,14,20,23,23,25,27,28,29,31,36,36,42[/tex]
There are 19 numbers, that means that the 10th value will be the number in the middle
This means that the median is 23
Janelle is making a poster. She cuts a triangle out of poster board. What is the area of the poster board that she has left?
The poster is a parallelogram, and it's area is:
A = bh
A = 20 x 10
A = 200 in.^2
Note: ^2 after in. means squared for area.
The area of the triangle that Janelle cut out of the poster board is:
A = 1/2bh
A = 1/2 x 10 x 9
A = 90/2
A = 45 in.^2
The area of the poster board that she has left is: 200 - 45 = 155 in.^2
Answer: 155 in.
The area of the poster board that she has left is,
⇒ 155 in²
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Now, The area of the parallelogram is,
⇒ Area of Parallelogram:
A= base × height
A= 20 in × 10 in
A= 200 in²
And, Area of Triangle:
A= 1/2 base * height
A= 1/2 (10 in)(9 in)
A= 1/2 (90)
A= 45 in²
Thus, The Area of Poster Left is,
A= Parallelogram Area - Triangle Area
A= 200 in² - 45 in²
A= 155 in²
Thus, 155 in² is the area of the poster board she has left.
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Micah made a scale model of the Empire State building.The building has an actual height of 381 meters. Micah’s model used a scale in which 1 cm represents 50 meters. what is the height in centimeters of Micahs model?
Answer:
Answer
3.0/5
8
1cm = 50
2 cm = 50 x 2
3cm = 50 x 3
and the inverse:50m = 50/50 = 1cm
100m = 100/50 = 2cm
150m = 150/50 = 3cm
381m = 381/
The height in centimeters of Micah's model given the scale of the drawing is 7.62cm
What is the height?A scale drawing is a reduced form in terms of dimensions of an original image / building / object
Scale of the drawing = original dimensions / dimensions of the scale drawing
The height of the model = 381 / 50 = 7,62cm
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If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is
Answer:
x=35
Step-by-step explanation:
ANSWER
x=35°
EXPLANATION
We want to find the value of x, when
[tex] \cos(x) = \sin(20 + x) \degree[/tex]
and 0°<x<90°
Recall that the sine and cosine are complementary trigonometric ratios.
Hence cos x = sin (90-x)
Our equation now, becomes;
[tex] \sin(90 - x) \degree= \sin(20 + x) \degree[/tex]
We now equate the argument to get,
[tex]90 - x=20 + x[/tex]
Group similar terms to obtain:
[tex]90 - 20 = x + x[/tex]
[tex]70 = 2x[/tex]
This implies that,
[tex]x = 35 \degree[/tex]
What are the coordinates of the endpoints of the mid segment for ABC that is parallel to Bc?
ANSWER ASAP PLEASE !!
Answer:
(4,2) and (8,2)
Step-by-step explanation:
The mid segment unites the middle of two sides of a triangle. In this case, the question wants us to have it parallel to BC, so it has to unite the middle of AB to the middle of AC.
The use of the clear grid in this case makes that we don't have to use any angle calculation.
If you start from point B, you'll need to go 6 units to the right and 8 units up to meet with A. That means the center point is located 3 units right and 4 units high from point B... so, we have point (4,2).
Starting from C, we do a similar calculation. you need to go 2 units to the left and 8 units up... so the mid-point is 1 unit to the left and 4 units up... so (8,2).
Which of the following is equivalent to the radical expression below, when the denominator has been rationalized and X >_ 5?
Answer:
Option D is correct.
Step-by-step explanation:
[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}\\[/tex] We need to rationalize this term and find the answer.
To rationalize the term we multiply and divide the above expression by [tex]\sqrt{x}+\sqrt{x-5}[/tex]
Solving:
[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}\\=\frac{10}{\sqrt{x}-\sqrt{x-5}} * \frac{\sqrt{x}+\sqrt{x-5}}{\sqrt{x}+\sqrt{x-5}} \\Multiplying\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{\sqrt{x}-\sqrt{x-5}*\sqrt{x}+\sqrt{x-5}}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{(\sqrt{x})^2-(\sqrt{x-5})^2}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{x-(x-5)}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{x-x+5)}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{5}\\=2*(\sqrt{x}+\sqrt{x-5})[/tex]
So, Option D is correct.
Answer:
The correct option is D) [tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex].
Step-by-step explanation:
Consider the provided radical expression.
[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}[/tex]
Multiply by the conjugate [tex]\frac{\sqrt{x}+\sqrt{x-5}}{\sqrt{x}+\sqrt{x-5}}[/tex]
[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{\left(\sqrt{x}-\sqrt{x-5}\right)\left(\sqrt{x}+\sqrt{x-5}\right)}[/tex]
[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{\left(x-(x-5))}[/tex]
[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{5}[/tex]
[tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex]
Hence, the correct option is D) [tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex].
Match the equation with its graph -4x + y = 8
Answer:
It will look like a graph with a slope of 4 and a y intercept of -8
Step-by-step explanation:
Just rearrange the variables
Answer:
Step-by-step explanation:
If the question mentions a graph, you'll need to share that graph.
Here's one good procedure for graphing -4x + y = 8:
Find the y-intercept: Let x = 0 and solve for y. We get (0, 8). Plot this.
Find the x-int. Let y = 0 and solve for x. We get (-2, 0). Plot this.
Then draw a straight line through these two points.
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Shiri is planting a 4-foot flower border around the edge of her yard. she drew this diagram to show how it should look.
what is the area of the flower border?
Answer:
384
Step-by-step explanation:
Answer:
They answer 256 because you will multiply the border four times (4x4x4x4) to get the perimeter of border.