Answer: The equations are
w + s = 4500
2.25s = 4500
Step-by-step explanation:
Let w represent the number of bottles of water that the football manager bought.
Let s represent the number of bottles of soda that the football manager bought.
The manager needs to buy a total of 4,500 drinks. This means that
w + s = 4500
He also needs to have 25% more water than soda.
25% of soda = 25/100 × s = 0.25s
25% more of water than soda = s + 0.25s = 1.25s
The equation would be
1.25s + s = 4500
2.25s = 4500
x=-4
Tell whether it’s graph is a horizontal or a vertical line
Answer:
Vertical Line
Step-by-step explanation:
A vertical line is x = [a number]
A horizontal line is y = [a number]
Answer:
vertical line
Step-by-step explanation:
A vertical line is of the form
x =
All the x values are the same and the y value changes
x = -4 is a vertical line
3. A tunnel is 300 feet deep and makes an angle of 30° with the ground, as shown below.
30°
300 feet
Tunne
How long is the tunnel?
Answer:
173.20 ft
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]
help please this is important
Answer:
D. [tex]3^3 - 4^2[/tex]
Step-by-step explanation:
Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2
2-x=-3(x+4)+6 please help
Answer:
2-x=-3x-12+6
2-x=-3x-6
8=-3x+x
8=-2x
x=-4
hope it's clear
mark me as brainliest
Answer:
X = -4Option B is the correct option.
Step by step explanation
2 - x = -3 ( x + 4) +6
Distribute -3 through the paranthesis
2 - x = - 3x - 12 + 6
Calculate
2 - x = - 3x - 6
Move variable to LHS and change its sign
2 - x + 3x = -6
Move constant to R.H.S and change its sign
- x + 3x = -6 - 2
Collect like terms and simplify
2x = -8
Divide both side by 2
2x/2 = -8/2
Calculate
X = -4
Hope this helps....
Good luck on your assignment..
Find the lateral area of a regular square pyramid if the base edges are of length 12 and the perpendicular height is 8.
Answer:
Lateral area of the pyramid = 120 square units
Step-by-step explanation:
In the figure attached,
A pyramid has been given with square base with edges of 12 units and perpendicular height as 8 units.
Lateral area of a pyramid = Area of the lateral sides
Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]
= [tex]\frac{1}{2}(\frac{b}{2})(\sqrt{(\frac{b}{2})^2+h^2})[/tex] [Since l = [tex]\sqrt{r^{2}+h^{2}}[/tex]]
= [tex]\frac{1}{2}(6)(\sqrt{6^2+8^2})[/tex]
= [tex]3\sqrt{100}[/tex]
= 30 units²
Now lateral area of the pyramid = 4 × 30 = 120 square units
Answer: 240 units^2
Step-by-step explanation:
LA= 1/2 Pl
P= perimeter of base
l= lateral height
l= 8^2 + (12/2)^2 = 10^2
P= 12 x 4 = 48
48 x 10 = 480
480/2 = 240
240 units^2
. If α and β are the roots of
2x^2+7x-9=0 then find the equation whose roots are
α/β ,β/α
Answer:
[tex]18x^2+85x+18 = 0[/tex]
Step-by-step explanation:
Given Equation is
=> [tex]2x^2+7x-9=0[/tex]
Comparing it with [tex]ax^2+bx+c = 0[/tex], we get
=> a = 2, b = 7 and c = -9
So,
Sum of roots = α+β = [tex]-\frac{b}{a}[/tex]
α+β = -7/2
Product of roots = αβ = c/a
αβ = -9/2
Now, Finding the equation whose roots are:
α/β ,β/α
Sum of Roots = [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]
Sum of Roots = [tex]\frac{\alpha^2+\beta^2 }{\alpha \beta }[/tex]
Sum of Roots = [tex]\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }[/tex]
Sum of roots = [tex](\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}[/tex]
Sum of roots = [tex]\frac{49}{4} + 9 /\frac{-9}{2}[/tex]
Sum of Roots = [tex]\frac{49+36}{4} / \frac{-9}{2}[/tex]
Sum of roots = [tex]\frac{85}{4} * \frac{2}{-9}[/tex]
Sum of roots = S = [tex]-\frac{85}{18}[/tex]
Product of Roots = [tex]\frac{\alpha }{\beta } \frac{\beta }{\alpha }[/tex]
Product of Roots = P = 1
The Quadratic Equation is:
=> [tex]x^2-Sx+P = 0[/tex]
=> [tex]x^2 - (-\frac{85}{18} )x+1 = 0[/tex]
=> [tex]x^2 + \frac{85}{18}x + 1 = 0[/tex]
=> [tex]18x^2+85x+18 = 0[/tex]
This is the required quadratic equation.
Answer:
α/β= -2/9 β/α=-4.5
Step-by-step explanation:
So we have quadratic equation 2x^2+7x-9=0
Lets fin the roots using the equation's discriminant:
D=b^2-4*a*c
a=2 (coef at x^2) b=7(coef at x) c=-9
D= 49+4*2*9=121
sqrt(D)=11
So x1= (-b+sqrt(D))/(2*a)
x1=(-7+11)/4=1 so α=1
x2=(-7-11)/4=-4.5 so β=-4.5
=>α/β= -2/9 => β/α=-4.5
Q4. A simple random sample of size n=180 is obtained from a population whose size=20,000 and whose population proportion with a specified characteristic is p=0.45. Determine whether the sampling distribution has an approximate normal distribution. Show your work that supports your conclusions.
Answer:
np = 81 , nQ = 99
Step-by-step explanation:
Given:
X - B ( n = 180 , P = 0.45 )
Find:
Sampling distribution has an approximate normal distribution
Computation:
nP & nQ ≥ 5
np = n × p
np = 180 × 0.45
np = 81
nQ = n × (1-p)
nQ = 180 × ( 1 - 0.45 )
nQ = 99
[tex]Therefore, sampling\ distribution\ has\ an\ approximately\ normal\ distribution.[/tex]
What is the area of this composite shape? Enter your answer in the box. in²
Answer:
53 in.
Step-by-step explanation:
to find the area u do 8 times 6 and 1/2 2(5)
triangle = 1/2bh
rectangle = bh
hope this helps
In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B?
Answer:
a) The student cannot receive an A in the class.
b) The student must score 119 in the third exams to make an A. This is clearly not possible, since he cannot make 119 in a 100-points exam.
c) The student can make a B but he must score at least 84 in the third exam.
Step-by-step explanation:
To make an A, the student must score 315 (350 x 90%) in both home and the three exams.
The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.
To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.
B ≥ 280 and < 315.
Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.
On a piece of paper, graph y + 2 ≤ -2/3x +4. Then determine which answer choice matches the graph you drew.
Answer:
B
Step-by-step explanation:
You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).
The shading is below the line because y-values are less than (or equal to) values on the line.
Choice B matches the attached graph.
Answer:
it is graph b
Step-by-step explanation:
If f(x) = 4x – 8 and g(x) = 5x + 6, find (f - g)(x).
Answer:
(f - g)(x) = -x - 14
Step-by-step explanation:
Step 1: Plug in equations
4x - 8 - (5x + 6)
Step 2; Distribute negative
4x - 8 - 5x - 6
Step 3: Combine like terms
-x - 14
Answer:
-x-14
Step-by-step explanation:
Hope this helps
g A cylindrical tank with radius 7 m is being filled with water at a rate of 6 mଷ/min. How fast is the height of the water increasing? (Recall: V = πrଶh)
Answer:
6/(49π) ≈ 0.03898 m/min
Step-by-step explanation:
V = πr²h . . . . formula for the volume of a cylinder
dV/dt = πr²·dh/dt . . . . differentiate to find rate of change
Solving for dh/dt and filling in the numbers, we have ...
dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min
dh/dt ≈ 0.03898 m/min
College students were given three choices of pizza toppings and asked to choose one favorite Results are shown in the table toppings Sremam 15 24 28 28 15 1 11 23 28 cheese meat 23 15 veggie Estimate the probability that a randomly selected student who is a junior or senior prefers veggie. Round the answer to the nearest thousandth
A. 371
B. 220
C. 395
D. 662
Answer:
B. 0.220
Step-by-step explanation:
The table is presented properly below:
[tex]\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|[/tex]
Number of junior students who prefers veggies =23
Number of senior students who prefers veggies =28
Total =23+28=51
Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie
=51/232
=0.220 (to the nearest thousandth)
The correct option is B.
units digit of the number[tex]2^{4000}[/tex]
Answer:
6
Step-by-step explanation:
We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:
[tex]2^{1}=2[/tex]
[tex]2^{2}=4[/tex]
[tex]2^{3}=8[/tex]
[tex]2^{4}=16[/tex]
[tex]2^{5}=32[/tex]
[tex]2^{6}=64[/tex]
[tex]2^{7}=128[/tex]
[tex]2^{8}=256[/tex]
...and so on
Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!
This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.
The answer is thus 6.
~ an aesthetics lover
Simplify the algebraic expression: 7x2 + 6x – 9x – 6x2 + 15. A) x2 + 15x + 15 B) x2 – 3x + 15 C) 13x2 + 3x + 15 D) x4 – 3x + 15
Answer:
B) [tex]x^2-3x+15[/tex]
Step-by-step explanation:
[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]
A) [tex]x^2+15x+15[/tex]
B) [tex]x^2-3x+15[/tex]
C) [tex]13x^2 + 3x + 15[/tex]
D) [tex]x^4-3x + 15[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
B. x² - 3x + 15
▹ Step-by-Step Explanation
7x² + 6x - 9x - 6x² + 15
Collect like terms
x² + 6x - 9x + 15
Subtract
x² - 3x + 15
Final Answer
x² - 3x + 15
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Using Volume Formulas: Tutorial
14 of 23 Save & Exit
Question 2
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single
rectangular pyramid. What values of land h for the four square pyramids and what values of I, w, and h for the rectangular pyramid will produce
identical volumes? There is more than one correct answer.
B
TUX
X
Font Sizes
A. A
E JE
Square Pyramids
Rectangular Pyramid
Volume
Base Length Height
Volume
Volume x4 Base Length Base Width Height
(2x)
3
(lxwh
3
I
Characters used: 110 / 15000
Submit
Answer:
For the Square
Base length is 6 units
Height is 4 units
Volume is 48 cubic units
Volume of 4 square pyramids is 192 cubic units
(Rectangular)
Base length is 12 units
Base width is 8 units
Height is 6 units
Volume is 192 cubic units
Step-by-step explanation:
Square pyramids is a geometric shape having square base. The appex is perpendicularly at the center of the square. If all the edges are equal it is equilateral square pyramid.
Rectangular pyramids have four sided base and four triangle sides that are coming together to the appex. Each base and appex form a triange called lateral face. The triangular faces are non rectangular base. Pyramid with n side have n + 1 vertices and 2n edges.
In a survery of 154 households, a Food Marketing Institute found that 106 households spend more than $125 a week on groceries. Please find the 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries.
Answer:
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 154, \pi = \frac{106}{154} = 0.6883[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 - 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.6151[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 + 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.7615[/tex]
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
When would you need to arrange polynomials
Find AC. (Khan Academy-Math)
Answer:
[tex]\boxed{11.78}[/tex]
Step-by-step explanation:
From observations, we can note that BC is the hypotenuse.
As the length of hypotenuse is not given, we can only use tangent as our trig function.
tan(θ) = opposite/adjacent
tan(67) = x/5
5 tan(67) = x
11.77926182 = x
x ≈ 11.78
Find the perimeter of the following trapezoid:
6 ft
2.5 ft/ 12 ft
2.5 ft
8 ft
Answer:
31ft
Step-by-step explanation:
6 ft + 2.5 ft + 12 ft + 2.5 ft + 8 ft = 31ft
I assumed the slash in the space between 2.5ft and 12ft was an error, so I ignored it in the solution to this problem.
Besides that, perimeter is found by adding all sides of the shape or figure together, and the sum of that is the perimeter.
The basic formula for perimeter is:
base + height + base + height.
I do not think you square perimeter as you do area (e.g. 31ft^2).
(a) Which unit fraction 1/n for n s 50 has the decimal expansion of longest period?
(b) Justify your reasoning
Answer:
0.02
Step-by-step explanation:
If n is 50, 1/n is equivalent to 1/50. 1/50 as a decimal is 0.02.
What is 1(y), when y=-7/12?
Answer: -7/12
Step-by-step explanation: an number multiplied by 1 is itself
A biologist samples and measures the length of the fish in a lake. What is the level of measurement of the data?
Answer:Ratio
Step-by-step explanation:
The ratio data because length has a true zero, and ratios of lengths are meaningful.
A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl
Answer: 7/8
Step-by-step explanation:
Let the boy is letter B and the girl is letter G.
So the possible outcomes are as follows below
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
SO the number of possible outcomes is 8
The number of outcomes where is at least 1 girl ( triples where is 1 girl, 2 girls or all 3 children are the girls) is 7
So the probability, that family with 3 kids has at least 1 girl is
P(number of girls >=1)= 7/8
Find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (1 comma 0 ), (3 comma 2 ), and (1 comma 2 )about the y-axis. Use the washer method to set up the integral that gives the volume of the solid.
Answer: Volume = [tex]\frac{20\pi }{3}[/tex]
Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be
V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]
For this case, the region generated by the conditions proposed above is shown in the attachment.
Because it is revolting around the y-axis, the formula will be:
[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]
Since it is given points, first find the function for points (3,2) and (1,0):
m = [tex]\frac{2-0}{3-1}[/tex] = 1
[tex]y-y_{0} = m(x-x_{0})[/tex]
y - 0 = 1(x-1)
y = x - 1
As it is rotating around y:
x = y + 1
This is R(y).
r(y) = 1, the lower limit of the region.
The volume will be calculated as:
[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]
[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]
[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]
[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]
[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]
[tex]V=\frac{20\pi }{3}[/tex]
The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].
Ann's $6,900 savings is in two accounts. One account earns 3% annual interest and the other earns 8%. Her total interest for the year is $342. How much does she have in each account?
Answer:
x=4200, y=2700
Step-by-step explanation:
let x be first account
y the second
x+y=6900
0.03x+0.08y=342
solve by addition/elimination)
multiply first equation by 0.03
0.03x+0.03y=207 subtract from second
0.03x+0.03y-0.03x-0.08y=207-342
0.05y=135
y=2700, x=4200
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 meters cubed A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? 10 meters cubed 20 meters cubed 30 meters cubed 40 meters cubed
Answer:
30 m^3
Step-by-step explanation:
Answer:
B. 20m3
Step-by-step explanation:
i dont know if its correct, hope it is tho
Hi, can someone help me on this. I'm stuck --
Answer:
a) Fx=-5N Fy=-5*sqrt(3) N b) Fx= 5*sqrt(3) N Fy=-5N
c) Fx=-5*sqrt(2) N Fy=-5*sqrt(2) N
Step-by-step explanation:
The arrow's F ( weight) component on axle x is Fx= F*sinA and on axle y is
Fy=F*cosA
a) The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(30)= -5 N Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N
b) Now the x component is co directed to axle x , and y component is opposite directed to axle y.
So x component is positive and y components is negative
So Fx = 10*sin(60)= 5*sqrt(3) N Fy= -10*cos(60)= -10*1/2= -5 N
c)The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(45)= -5*sqrt(2) N
Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N
Please help ASAP thanks in advance
Answer:
Make a point at (3pm, 45), (4.5 pm, 45), (5.5pm, 30), (6.5pm, 15), and (7.5pm, 0). Then connect the dots starting at (0,0) Then you have your graph :)
Step-by-step explanation:
Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1). g
Complete Question:
Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)
Answer:
Directional derivative at point (1,3), [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]
Step-by-step explanation:
Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)
g(x,y) = [tex]x^2y^5[/tex]
[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]
[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]
Let P = (1, 3) and Q = (3, 1)
Find the unit vector of PQ,
[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]
[tex]|\bar{PQ}| = \sqrt{8}[/tex]
The unit vector is therefore:
[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]
The directional derivative of g is given by the equation:
[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]