To do this, you can first express the percentages as decimals, like this
[tex]\begin{gathered} 60\text{ \%}=\frac{60}{100}=0.6 \\ 85\text{ \%}=\frac{85}{100}=0.85 \\ 70\text{ \%}=\frac{70}{100}=0.7 \end{gathered}[/tex]Later, you can take
x = number of ounces of solution A
y = number of ounces of solution B
And build the following system of linear equations
[tex]\begin{gathered} \mleft\{\begin{aligned}x+y=180 \\ 0.6x+0.85y=0.7\cdot180\end{aligned}\mright. \\ \mleft\{\begin{aligned}x+y=180 \\ 0.6x+0.85y=126\end{aligned}\mright. \end{gathered}[/tex]To solve it you can use the substitution method, for example.
Solve for x from the first equation and substitute this value in the second equation
[tex]\begin{gathered} x+y=180 \\ \text{ Subtract y from both sides of the equation} \\ x+y-y=180-y \\ x=180-y \end{gathered}[/tex]Now substituting in the second equation
[tex]\begin{gathered} 0.6(180-y)+0.85y=126 \\ 108-0.6y+0.85y=126 \\ 108+0.25y=126 \\ \text{ Subtract 108 from both sides of the equation} \\ 108+0.25y-108=126-108 \\ 0.25y=18 \\ \text{ Divide both sides of the equation by }0.25 \\ \frac{0.25y}{0.25}=\frac{18}{0.25} \\ y=72 \end{gathered}[/tex]Now plug the value of y into the first equation
[tex]\begin{gathered} x+y=180 \\ x+72=180 \\ \text{ Subtract 72 from both sides of the equation} \\ x+72-72=180-72 \\ x=108 \end{gathered}[/tex]So,
[tex]\mleft\{\begin{aligned}x=108 \\ y=72\end{aligned}\mright.[/tex]Therefore, the scientist should use 108 ounces of solution A and 72 ounces of solution B.
A vertical tower is 20 m high from the horizontal ground. The angle of depression of aball from the top of the tower is 42°. Calculate the distance, in m, of the ball from thebase of the tower
ANSWER
22.2 m
EXPLANATION
Let us make a sketch of the problem.
From the diagram:
T = top of the tower
B = Ball
O = Base of the tower
Now, we have to find x, which is the distance from the ball to the base of the tower.
Since the angle of depression is 42°, it means that angle
To find x, we can apply Pythagoras Rule:
[tex]\begin{gathered} \tan (<\text{OTB) = }\frac{x}{20} \\ \Rightarrow\text{ x = 20 }\cdot\text{ tan(48)} \\ x\text{ = 20 }\cdot\text{ 1.11} \\ x\text{ = 22.2 m} \end{gathered}[/tex]The distance of the ball from the base of the tower is 22.2 m
I need help with this question
Let:
[tex]\begin{gathered} B=(3,2) \\ B^{\prime}=(-2,-2) \\ \end{gathered}[/tex]After a translation 5 units left
[tex]B\to(3-5,2)\to(-2,2)[/tex]and after a reflection across the x-axis:
[tex]B\to(x,-y)\to(-2,-2)[/tex]A cone has a volume V, a radius r, and a height of 12 cm. a.) A cone has the same height and of the radius of the original cone. Write an expression for it's volume. b.) A cone has the same height and 3 times the radius of the original cone. Write an expression for its volume.
expressionGiven from the original,
Volume=V; radius= r and height = 12cm
Please note that the volume V, of a cone, is calculated with the formula
[tex]\begin{gathered} The\text{Volume of a Cone= }\frac{1}{3}\times Circular\text{ Base Area}\times\text{Height} \\ =\frac{1}{3}\times\Pi r^2\times h \end{gathered}[/tex]For question (a)
height is the same as the original but the radius is
[tex]\text{new radius,R= }\frac{1}{3}of\text{ r=}\frac{1}{3}\times r=\frac{r}{3}[/tex]The expression for the new volume will give us
[tex]\begin{gathered} \text{Note, V}_{cone}=\frac{1}{3}\times\Pi R^2\times H \\ H=h=12;\text{ R=}\frac{r}{3} \\ The\text{ New Volume=}\frac{1}{3}\times\Pi\times(\frac{r}{3})^2\times12 \\ =\frac{1}{3}\times3.14\times\frac{r^2}{9}\times12 \\ =\frac{37.68r^2h}{27} \\ =1.396r^2cm^3 \end{gathered}[/tex](a) Therefore, The expression for the new volume is 1.396r²cm³
(b) At this time, the height has the height as the original cone but 3 times the radius of the original cone.
Note that the new height still remains as h, while the new radius will be
[tex]\begin{gathered} \text{New height= h} \\ Then\text{ew radius= 3}\times r=3r \end{gathered}[/tex]Substituting the new height and the new radius into the formula for the volume of the cone will give
[tex]\begin{gathered} V_{cone}=\frac{1}{3}\times\Pi\times r^2\times h \\ \text{the new radius =3r and the new height is still h} \\ V_{cone}=\frac{1}{3}\times\Pi\times(3r)^2\times12 \\ =\frac{1}{3}\times3.14\times9r^2\times12 \\ =\frac{3.14\times9r^2\times12}{3} \\ =113.04r^2cm^3 \end{gathered}[/tex](b) Therefore, the expression for the new volume is 113.04r²cm³
Select the letter that correctly identifies the base of the prism.A. cB. dC. bD. a
ANSWER
D. a
EXPLANATION
A prism has two faces that are equal. These are called base and top (usually referred to as base as well), and their shape defines the name of the prism - for example, triangular prism or rectangular prism.
The other faces are all rectangles.
In this figure, we can see that b, c, and d are rectangular faces, so none of these is the base. Hence, a is the base of the prism.
See attached I wasn’t able to write all the characters:Suppose r and p are true, and the statements s and t are false. Indicate the truth value of each statement. Do not construct a truth table
r and p = true
s and t = false
The logical expression is given by
[tex](p\wedge t)\leftrightarrow(p\rightarrow s)[/tex]Let us solve the above expression.
(p ∧ t) means p and t
(p ∧ t) is true if p and t both are true.
But we know that both p and t are not true since t is false.
So, (p ∧ t) is false.
(p -> s) means p implies s
(p -> s) is true if p is false or s is true.
But we know that p is true and s is false.
This means that (p -> s) is false.
Finally,
↔ means equivalent
(p ∧ t) ↔ (p -> s) is true if both are true or both are false.
We know that (p ∧ t) is false and (p -> s) is false
So, (p ∧ t) ↔ (p -> s) is true since both of them are false.
U={1,2,3,4,5,6,7,8}A={2,5,6}B={2,3,4,8}C={1,4,7} use the roster method AU(BUC)
The set BUC is a new set with the elements of set B and C:
[tex]B\cup C=\mleft\lbrace1,2,3,4,7,8\mright\rbrace[/tex]Now, AU(BUC) is the union of the elements in A and in BUC:
[tex]A\cup(B\cup C)=\mleft\lbrace_{}1,2,3,4,5,6,7,8\mright\rbrace[/tex]determine the domain of each functions y=3/2
The equation is given
[tex]y=\frac{3}{2}[/tex]The domain of each functions y=3/2 is
[tex]D=(-\infty,\infty)[/tex]
s 1 05 1 -1.5 -05 0.5 1 -0.5 -1.5 If the cosine of in this unit circle is a, what would be true of the cosine of in a circle with a radius of 2?
In the unit circle
[tex]\cos ^2x+\sin ^2x=1[/tex][tex]x^2+y^2=r^2[/tex]Where r is the radius of the circle
x- coordinate represents cos angle
cos angle = x/r
Since r = 2
cos angle = x/2
y-coordinate represents sin angle
sin angle = y/r
sin angle = y/2
Because the question is incomplete
we can not find which is true
Would the top be 1 and the bottom be 6
2÷ 0
We cannot divide by 0
Take a piece of paper and cut it into zero pieces.
We cannot do that. We will still have pieces of paper.
We cannot divide by 0
2 ÷ 0 = undefined
0 ÷ 6
If you start with 0 and divide by something, you will still have 0
You cannot divide nothing into something
0 ÷ 6 = 0
The coordinate plane shown below shows the locations of the library and park in the town where Rasheed lives. 5 Library 4 2 1 -4 -3 -1 2 4 3 5 -1 -2 Park 5 Which expression represents the distance from the library to the park as modeled on the coordinate grid?
Notice that both the Library and the Park lie on the same vertical line.
Then, to find the distance, count how many units apart are they, or substract their y-coordinates.
The y-coordinate of the Library is 5 while the y-coordinate of the Park is -3. Then, the difference is:
[tex]5-(-3)=5+3=8[/tex]Therefore, the distance between the Library and the Park is:
[tex]8[/tex]Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:A. 19 pB. 20 pC. 21 pD. 18 p
Given that:
• Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play.
• A score consecutive number of points from smallest to greatest in respect to the order of the names: Louise Tammy Dolores and Cheryl.
Let be:
- The number of points that Louise scored in the tennis matches:
[tex]n[/tex]- The number of points that Tammy scored in the tennis matches:
[tex]n+1[/tex]-The number of points that Dolores scored in the tennis matches:
[tex]n+2[/tex]- The number of points that Cheryl scored in the tennis matches:
[tex]n+3[/tex]You can set up the following equation to represent the total number of points they scored in the tennis matches:
[tex]n+(n+1)+(n+2)+(n+3)=78[/tex]Now you can solve for "n":
[tex]n+n+1+n+2+n+3=78[/tex][tex]4n+6=78[/tex][tex]4n=78-6[/tex][tex]\begin{gathered} n=\frac{72}{4} \\ \\ n=18 \end{gathered}[/tex]Hence, the answer is: Option D.
Write and solve an equation. 1. A number t plus 32 is 652. A number b added to 13 is equal to 75.2
1)
A number plus 32 is 65 can be written as t+32=65; then,
[tex]\begin{gathered} t+32=65 \\ \Rightarrow t+32-32=65-32=33 \\ \Rightarrow t=33 \end{gathered}[/tex]The answer is t=33.
2)
A number b added to 13 is equal to 75.2 can be written as 13+b=75.2; therefore,
[tex]\begin{gathered} 13+b=75.2 \\ \Rightarrow-13+13+b=-13+75.2=62.2 \\ \Rightarrow b=62.2 \end{gathered}[/tex]The answer is b=62.2
Profit, P(x), is the difference between revenue, R(2), and cost, C(2), so P(x) = R(x) - C(x) whichexpression represents P(x), if R(x) = 2x4 - 3x + 2x – 1 and C(x) = x4 – x2 + 2x + 3?
Given:
[tex]\begin{gathered} P(x)=R(x)-C(x) \\ R(x)=2x^4-3x+2x-1 \\ C(x)=x^4-x^2+2x+3 \end{gathered}[/tex]Substitute the expression of R(x) and C(x) in the expression of P(x).
[tex]\begin{gathered} P(x)=2x^4-3x+2x-1-(x^4-x^2+2x+3) \\ P(x)=2x^4-3x+2x-1-x^4+x^2-2x-3 \\ P(x)=(2x^4-x^4)+(-3x+2x-2x)+(x^2)-3-1 \\ P(x)=x^4(2-1)+x(-3+2-2)+x^2-4 \\ P(x)=x^4\times1+x\times-3+x^2-4 \\ P(x)=x^4-3x+x^2-4 \\ P(x)=x^4+x^2-3x-4 \end{gathered}[/tex]Thus, the above expression of P(x) represents the simplest expression of P(x).
23. S is the sum of the first 100 consecutive positive even integers, and T' is the sum of the first 100 consecutive positive integers. S is what percent greater than 7?A. 100%B. 50%C.10%D.2%
S is the sum of the first 100 consecutive positive even integers, and T' is the sum of the first 100 consecutive positive integers. S is what percent greater than T?
A. 100%
B. 50%
C.10%
D.2%
we have that
t=1/2 * n(n+1) = sum all numbers from 1 to n
For n=100
t=1/2 * 100(100+1)=5,050
s=n(n+1) = sum 1st n even numbers
s=100(100+1)=10,100
so
s/t=10,100/5,050
s/t=2
therefore
the answer is 100%option AA 12 -ounce can of fizzy cola has a mean volume of 12oz with a standard deviation of 0.25oz harry opens a can and measures and fines he has less than 11.5 oz of cola. What’s the probability of this occurring?
Given:
[tex]\begin{gathered} Mean=12 \\ Standarddeviation=0.25 \end{gathered}[/tex]To Determine: The probability of a measures that has less than 11.5
Solution
The formula for finding the z for a one sample of a random distribution is given as
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Ginny's median score on three test was 90. Her mean score was 92 and her range was 6. what were here three test scores?
let x, y, z be the three test scores
[tex]\frac{x+y+z}{3}=92[/tex]y is the median, y = 90
If the range is 6, then;
z - x = 6
Make z subject of formula from z - x = 6
z = 6+ x
substitute y =90 and z = 6+ x into our first equation and then solve for x
[tex]\frac{x+90+6+x}{3}=\text{ 92}[/tex][tex]\frac{2x+96}{3}=92[/tex]Multiply bothside by 3
[tex]2x\text{ + 96 =276}[/tex]subtract 96 from bothside
[tex]2x\text{ =180}[/tex]Divide bothside by 2
[tex]x=\frac{180}{2}[/tex][tex]x=90[/tex]substitute x =90 into z = 6+ x
z = 6 + 90 =96
The three test scores are;
90, 90, 96
M R 3 5 N 6 10. B S 6 L 7 ALMN А E 6 D B 8 20 20
8) To see if the triangles are similar que hace to calculate the ratio beetwen the side so:
[tex]\begin{gathered} \frac{5}{6}=\frac{6}{7}=\frac{3}{4} \\ 0.83=0.88=0.75 \end{gathered}[/tex]So the ratios are nor constant so the triangles are not similar
-4x-2y=-124x+8y=-24How do I solve each system by elimination?
Given:
[tex]\begin{gathered} -4x-2y=-12\ldots.(1) \\ 4x+8y=-24\ldots\text{ (2)} \end{gathered}[/tex]Add equation (1) and (2)
[tex]-4x-2y+4x+8y=-12-24[/tex][tex]6y=-36[/tex][tex]y=-6[/tex]Substitute y=-6 in (2)
[tex]4x+8(-6)=-24[/tex][tex]4x-48=-24[/tex][tex]4x=48-24[/tex][tex]x=6[/tex]Identify the type of observational study. A researcher plans to obtain data by examining the financial transactions of victims who perished in a tornado.Choose the correct type of observational study below.A. retrospectiveB. cross-sectionalC. prospective
Take into account that a retrospective study looks backwards and examines different types of situations based on previous results.
Based in the previous definition, you can conclude that for the given case, the type of observational study is
A. retrospective
because the information is about situations in the past
Evaluate the integral and interpret it as the area of a region
ANSWER:
0.90168
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\int ^1_{-1}\mleft|4^x-2^x\mright|dx\: [/tex]We first solve the integral and then evaluate it, like this:
[tex]\begin{gathered} \int ^1_{-1}\mleft|4^x-2^x\mright|dx\: =\int ^0_{-1}(-4^x+2^x)dx+\int ^1_0(4^x-2^x)dx \\ \int ^0_{-1}(-4^x+2^x)dx=-\int ^0_{-1}4^xdx+\int ^0_{-1}2^xdx=\mleft[-\frac{4^x}{\ln\:\:\:\left(4\right)}+\frac{2^x}{\ln\:\:\:\left(2\right)}\mright]^0_{^{}-1} \\ \int ^1_0(4^x-2^x)dx=-\int ^1_04^xdx-\int ^1_02^xdx=\mleft[\frac{4^x}{\ln\:\left(4\right)}-\frac{2^x}{\ln\:\left(2\right)}\mright]^1_{^{}0} \end{gathered}[/tex]We evaluate for each interval:
[tex]\begin{gathered} \mleft[-\frac{4^x}{\ln \mleft(4\mright)}+\frac{2^x}{\ln \mleft(2\mright)}\mright]^0_{^{}-1}=-\frac{4^0}{\ln (4)}+\frac{2^0}{\ln (2)}+\frac{4^{-1}}{\ln (4)}-\frac{2^{-1}}{\ln (2)}=\frac{1}{8\ln \mleft(2\mright)} \\ \mleft[\frac{4^x}{\ln \mleft(4\mright)}-\frac{2^x}{\ln \mleft(2\mright)}\mright]^1_{^{}0}=\frac{4^1}{\ln (4)}-\frac{2^1}{\ln (2)}-\frac{4^0}{\ln (4)}+\frac{2^0}{\ln (2)}=\frac{1}{2\ln\left(2\right)} \\ \frac{1}{2\ln\left(2\right)}+\frac{1}{8\ln\left(2\right)}=\frac{5}{8\ln\left(2\right)}\cong0.90168 \end{gathered}[/tex]The value of the integral is 0.90168 and represents the area of the region.
Determine whether the given ordered pair is a solution to the system of equations. 6x−2y =30 −3x+3y =15 and (10,15)
Explanation
We have the simultaneous equation
[tex]\begin{gathered} 6x-2y=30---equation\text{ 1} \\ -3x+3y=15---equation\text{ 2} \end{gathered}[/tex]To check if (10,15) is a solution, we will have to substitute
x=10 and y=15
into both equations and check if it is true
So for equation 1
[tex]\begin{gathered} 6(10)-2(15)=30 \\ True \end{gathered}[/tex]Next, for the second equation
[tex]\begin{gathered} -3(10)+3(15)=15 \\ True \end{gathered}[/tex]Thus,
We can conclude that (10,15) is a solution
2. Carole was scuba diving and descending 4.5 feet per second. If she stopped to look at coral that are 36.9 ft below the surface, how long did it take?
Speed = distance / time
time = distance / speed
Distance = 36.9 ft
Speed = 4.5 feet per second
Replacing:
Time = 36.9 / 4.5 = 8.2 seconds
Hey! Can anyone help me with my practice worksheet question?
Since the inequality has a greater or equal sign, the boundary line of inequality must be a solid line.
So, options on the left side are out.
Now, it says that y ≥ 1-3x, so the shaded area must be above the y-axis.
Test a point to see if it satisfies the inequality:
x=0 and y =0 ; y ≥ 1-3x
0 ≥ 1-3(0)
0 ≥ 1
Since the point doesn't satisfy the inequality, point (0,0) doesn't belong to the shaded region.
Correct option is the top right one.
Find the equation of line from the given graph:
Answer:
[tex]y(x)=\frac{3}{4}x-\frac{18}{4}[/tex]
Explanation: We need to write the equation of the line which has the general form:
[tex]y(x)=mx+b[/tex]Where:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ b=y-\text{intercept} \end{gathered}[/tex]These two parameters are found as follows:
Slope:
[tex]\begin{gathered} P_1(-2,-6) \\ P_2(2,-3) \\ \therefore\rightarrow \\ m=\frac{\Delta y}{\Delta x}=\frac{-6-(-3)}{-2-2}=\frac{-3}{-4}=\frac{3}{4} \end{gathered}[/tex]y-intercept:
From the graph, it is the point where the line intersects the y-axis, therefore it is:
[tex]\begin{gathered} y(-2)=-6=\frac{3}{4}(-2)+b \\ \therefore\rightarrow \\ b=-6+\frac{6}{4}=\frac{-24+6}{4}=\frac{-18}{4}=-4.5 \end{gathered}[/tex]And the graph agrees with it:
Equation of line is:
[tex]y(x)=\frac{3}{4}x-\frac{18}{4}[/tex]What is 12 = 4 + 7 x 8
Answer:
Step-by-step explanation:
PEMDAS
find the sum of the angle measures of each polygon 50 - gon
To be able to find the sum of all angles in a 50 - gon, we will be using the following formula:
[tex]\text{ (n - 2) x 180}[/tex]Where,
n = number of sides = 50
We get,
[tex]\text{ (n - 2) x 180}[/tex][tex]\text{ = (50 - 2) x 180}[/tex][tex]\text{ = 48 x 180}[/tex][tex]\text{ = 8,640}^{\circ}[/tex]Therefore, the sum of all angles inside a polygon is 8,640
Answer:
8640°
Step-by-step explanation:
Formula: 180(n-2) = 180(50-2) = 8640
What is the equation of the circle shown?785432.А1-B-8-5-4-3-2-1 02.4-1-2-3-4-5(x2 + (y)2 =IIWord Bank:10 -2 5 + 2 - 1+ 1 25Blank 1:Blank 2:Blank 3:
Consider that the equation of a circle with center (h,k) and radius 'r' units, is given by,
[tex](x-h)^2-(y-k)^2=r^2[/tex]Observe the given diagram carefully.
The center of the circle lies at (-2,1),
[tex](h,k)=(-2,1)[/tex]The radius of the circle is the distance of any point on the circle from the center. Since the point (3,0) lies on the circle, the radius is calculated as,
[tex]r=3-(-2)=3+2=5[/tex]Substitute the values in the standard equation of circle,
[tex]\begin{gathered} (x-(-2))^2-(y-1)^2=5^2 \\ (x+2)^2-(y-1)^2=25 \end{gathered}[/tex]Thus, the equation of the given circle is,
[tex](x+2)^2-(y-1)^2=25[/tex]Which of the following shows the simplified function of sec x sin?
we have the expression
[tex]secxsin(\frac{\pi}{2}-x)[/tex]Remember that
[tex]sin(A-B)=sinAcosB-cosAsinB[/tex]therefore
[tex]\begin{gathered} sin(\frac{\pi}{2}-x)=sin\frac{\pi}{2}cosx-cos\frac{\pi}{2}sinx \\ \\ sin(\frac{\pi}{2}-x)=cosx \end{gathered}[/tex]substitute in the given expression
[tex]\begin{gathered} secx(cosx) \\ (\frac{1}{cosx})cosx \\ 1 \end{gathered}[/tex]The answer is 1I need help with the steps to solve the attach problem in the photo.
• We are told that there were 3/8 in the begining , where 3 is the number of advaced maths and 8 is the number of regular maths .
,• 4 /7 were the final results . meaning 4 advanced and 7 regular maths
,• 4/7 : 92/x ( where x is final advanced, and x is the regular maths )
so, 3+8 = 11 and 4+7 = 11
if 92 students are equal to 4 in the final ratio;
92 / 4 = 23 in the ratio of 1
therefore :
if 4 : 92
then 7 : 23
7 x 23 = 161 students in regular maths
161 + 92 = 253 students in total
(extra notes :if you want to find the original class numbers
253 /11 = 23
23 X 3 = 69
23 X8 = 184
this means that there were 69 advanced and 184 regular students)
Identify at least two values of t at which the inequality B(t) < A(t) is true
we have that
For t > 6 years-------> B(t) < A(t)
therefore
For t=7 and for t=8 ------> B(t) < A(t)