Simply divide 1.75 by 5 to find that 0.35 mL of water will be in each beaker.
two business partners, Ellen and Bob, invested money in their business at a ratio of 3 to 7. Bob invested the greater amount. the total amount invested was 200 dollars. how much did each partner invest?
Answer:
Ellen invested $60 and Bob invested $140
Step-by-step explanation:
let the two amounts invested by 3x and 7x
(notice 3x : 7x = 3 : 7 )
then 3x + 7x = 200
10x = 200
x = 20
then 3x = 3(20) = 60
and 7x = 7(20) = 140
60+140=200
Ellen invested $60, and Bob invested $140 in their business.
The student's question involves determining how much each business partner invested in their business based on a given ratio and total investment amount. Ellen and Bob invested money at a ratio of 3 to 7 with a total of $200 invested. To solve this, we need to find out what each 'part' of the ratio is worth in dollars.
Let's consider the total number of parts in the ratio, which is 3 (for Ellen) + 7 (for Bob) = 10 parts in total. Since the total amount invested is $200, each part of the ratio is worth $200 divided by 10, which is $20. Therefore:
Ellen invested 3 parts: 3 parts * $20 per part = $60.Bob invested 7 parts: 7 parts * $20 per part = $140.Hence, Ellen invested $60, and Bob invested $140 in their business.
A iron worker will cut 2.4 meters of a iron rod into 4 smaller rods. The smaller rods will all be the same length. What should the length of the 4 smaller rods be?
Answer:
.6 meters
Step-by-step explanation:
We need to take the total length and divide it by 4, since that is the number of rods we want and they are all the same length
2.4/4 =.6 meters
Each rod will be .6 meters long
according to a recipe each batch of pancake mix can make 12 pancakes Kathy is making 3 batches for a brunch party. if each batch needs 7/12 cups of milk how much milk does she need in total?
The answer is 1 and 3/4 because if you divide 21 by 12 you get 1.75 convert the decimal into a fraction and get 1 and 3/4. :)
She will need 1 3/4 cups of milk
Number of batches of pancake to be made = 3 batches
Number of cups of milk needed for each batch = 7/12
Therefore, in order to get the total number of cups of milk needed for the batches will be calculated thus:
= 7/12 × 3
= 21/12
= 1 9/12
= 1 3/4
Therefore, she will need 1 3/4 cups of milk.
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what is the midpoint of the segment shown below? (-3,4) (-6,-1)
Answer:
-9/2 , 3/2
Step-by-step explanation:
The coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).
What are the coordinates of the midpoint of the line segment AB?Suppose we've two endpoints of a line segment as A(p,q), and B(m,n), then let the midpoint be M(x,y) on that line segment. Then, its coordinates are x =(p+m)/2 and y = (q+n)/2.
Given the endpoints of the line segment are A(-3,4) and B(-6,-1), then the coordinates of the midpoint will be,
x = (-3-6)/2 = -9/2 = -4.5
y = (4-1)/2 = 3/2 = 1.5
Hence, the coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).
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plzzz help me with this question look at picture
ANSWER
B. 81
EXPLANATION
The given expression is:
[tex] {3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } [/tex]
Recall that:
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
We simplify the expression using the properties of exponents to obtain:
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11}{5} - - \frac{9}{5} } [/tex]
We simplify the exponents to get;
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11 + 9}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{20}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{4} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = 81[/tex]
The correct answer is B. 81
What is the slope of the line that is represented by the equation y−15=−6(x+7)?
Enter your answer as a number, like this: 42
Or, if your answer is a fraction, such as 314, enter it like this: 3/14
Answer:
slope = - 6
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 15 = - 6(x + 7) ← is in point- slope form
with slope m = - 6
The slope of the line that is represented by the equation y-15=-6(x+7) is -6.
The given equation is y-15=-6(x+7).
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The standard form of the slope intercept form is y=mx+c.
Where, m=slope and c=y-intercept
Here, y-15=-6(x+7) can be written as y-15=-6x-42
⇒ y=-6x-42+15
⇒ y=-6x-27
So, slope of an equation is -6.
Therefore, the slope of the line that is represented by the equation y-15=-6(x+7) is -6.
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Emilee signed a finance agreement for her purchase what is the total amount she will pay back under this agreement
To calculate the total amount Emilee will pay back under a finance agreement, one needs to know the specifics of the loan. Joanna's example, with a known interest rate and term, shows how to use the present value of an annuity formula to find out the maximum loan and total amount paid over time.
Explanation:The question pertains to calculating the total amount that Emilee will pay back under a finance agreement for her purchase. To determine this amount, one must know the principal amount of the loan, the interest rate, and the term of the loan.
For instance, if Joanna can afford to pay $12,000 a year for a house loan at an annual interest rate of 4.2% for 30 years, one can use the formula for the present value of an annuity to calculate the maximum loan she can afford. The formula is PV = PMT [1 - (1 + i)^(-n)] / i, where PV is the present value (the maximum loan), PMT is the annual payment ($12,000), i is the interest rate per period (4.2% annually), and n is the number of periods (30 years).
By applying this formula, Joanna can afford a maximum loan of approximately $202,556.98. Over 30 years, she will end up paying $12,000 times 30, which equals $360,000 in total. Similarly, to determine the total amount Emilee will repay, the same types of calculations would apply based on the terms of her finance agreement.
Answer: $1308
Step-by-step explanation: APEX
12 monthly payments of $109 = $1308
A map is drawn using the scale 2 cm:100 mi. On the map, Town B is 3.5 centimeters from Town A, and Town C is 2 centimeters past Town B. How many miles apart are Town A and Town C?
A.) 275 miles
B.) 200 miles
C.) 550 miles
D.) 1,100 miles
Answer:
275 miles
Step-by-step explanation:
3.5 cm = 175 and 2 more centimeters past that is 100 so 175 +100=275
so your answer is a 275 miles
A line passes through the point (0, 2) and has a slope of -1/2. What is the equation of the line?
A) 2x+y=4
B)x-2y=4
C)x+2y=4
Answer:
C) x + 2y = 4Step-by-step explanation:
The slope-intercept form:
y = mx + b
m - slope
b - y-intercept (0, b)
We have (0, 2) → b = 2 and m = -1/2. Substitute:
y = -1/2x + 2 multiply both sides by 2
2y = -x + 4 add x to both sides
x + 2y = 4
Based on the function F(x)=x^4-3x^2-1 and the graph of G(x) below, which of the following statements is true
Analyzing the given function F(x), we can predict that it is a quartic function with various possible shapes and intersection points with the x-axis. However, a comparison or correlation to function G(x) cannot be accurately made without additional information about graph G(x).
Explanation:Given the function F(x)=x^4-3x^2-1 and the unspecified G(x) graph, it's difficult to make an accurate statement without observing the shape, slope, and specific points on the G(x) graph. However, by understanding the given function F(x), we can still provide some insights. The function F(x) here is a quartic function (as the largest exponent is 4). The graph of a quartic function can have various shapes - it may have zero, one or two extreme points, and it may pass through the x-axis at zero, two or four points. It is essential to look at two-dimensional graphing to properly analyze and correlate F(x) and G(x).
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what is the average rate of change for this quadratic function for the interval from x= -4 to x= -2
Answer:
B. 6.
Step-by-step explanation:
We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].
We will use formula [tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(-2)-f(-4)}{-2--4}[/tex]
[tex]\text{Average rate of change}=\frac{6--6}{-2+4}[/tex]
[tex]\text{Average rate of change}=\frac{6+6}{2}[/tex]
[tex]\text{Average rate of change}=\frac{12}{2}[/tex]
[tex]\text{Average rate of change}=6[/tex]
Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.
Answer:
6
Step-by-step explanation:
just took on A P E X
Use a calculator to find the value of each expression. Round your answer to the nearest hundredth.
11. Arcsin(1/5)
12. Arcsin(-0.34)
13. Arcsin(0.6)
Answer:
Arcsin(1/5) = 0.20
Arcsin(-0.34) = -0.35
Arcsin(0.6) = 0.64
Step-by-step explanation:
Using a calculator we can find the value of each expression:
Arcsin(1/5) = 0.20135792079, rounding to the nearest hundredth we have that: Arcsin(1/5) = 0.20.
Arcsin(-0.34) = -0.346916897527, rounding to the nearest hundredth we have that: Arcsin(-0.34) = -0.35
Arcsin(0.6) = 0.643501108793, rounding to the nearest hundredth we have that: Arcsin(0.6) = 0.64
We found the arc-sin (or inverse sine) of three different values using a calculator, rounding to the nearest hundredth decimal place: Arcsin(1/5) is approximately 0.20, Arcsin(-0.34) is -0.34, and Arcsin(0.6) is about 0.64.
Explanation:The student asked to find the arc-sine (inverse sine) of three values and round the answers to the nearest hundredth. You use your calculator to find these values:
Arcsin(1/5): When you input this into your calculator, you'll get a value of approximately 0.201. So, arc-sin of 1/5 is about 0.20,Arcsin(-0.34): Inputting this into your calculator gives an approximate value of -0.344. So, arc-sin of -0.34 is around -0.34,Arcsin(0.6): Inputting this into your calculator gives about 0.643. So, arc-sin of 0.6 is approximately 0.64.Note: Arcsine is a trigonometric function which checks the angle whose sine is a given number.
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how to find slope??................................
y2-y1/x2-x1
Y(subscript 2) - Y(subscript 1) / X(subscript 2) - X(subscript 1)
The formula for slope is the difference in y-values divided by the difference in x-values. the slope of a line is its steepness or its rate of change. There are 4 types of slopes positive, negative, zero, and undefined.
5x - 2y = 3
-5x + 4y = 9
Solve the system of equations.
A) x = 6, y = 3
B) x = 6, y = 13
1
2
C) x = 3, y = 6
D) x = 1, y = 0
Answer: Your answer is c
Step-by-step explanation: The first thing you can do is add the two equations together to cancel out x
5x-2y=3
-5x+4y=9
added them together will get us 2y=12, from here divide 2 and get y=6
Plug 6 into the first equation and solve for x.
5x-2(6)=3
5x-12=3, add 13 to the other side
5x=15, divide 5 and get the answer
x=3
Waves with an amplitude of 2ft pass a doc every 30 seconds. Write an equation for a cosine model the height of a water particle above and below the mean water line
[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{C}{B}\\ ~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}[/tex]
[tex]\bf \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)[/tex]
with that template in mind, let's see.
[tex]\bf \stackrel{A = 2}{g(x) = 2cos(Bx+C)}\qquad \begin{cases} \stackrel{\textit{period of 30 seconds}}{\cfrac{2\pi }{B}=30}\\\\ \cfrac{2\pi }{30}=B\\\\ \cfrac{\pi }{15}=B \end{cases}\implies g(x)=2cos\left( \frac{\pi }{15}x+C \right)[/tex]
now, since the period is 30, and cos(x) starts off at 1, recall cos(0) = 1, so then le'ts move the starting point over by simply doing a horizontal shift to the right by a quarter of the period, 30/4 = 15/2 units, that way the initial "hump" starts off at 0.
[tex]\bf \stackrel{\textit{horizontal shift of }\frac{15}{2}}{\cfrac{15}{2}=\cfrac{C}{B}}\implies \cfrac{15}{2}=\cfrac{C}{~~\frac{\pi }{15}~~}\implies \cfrac{15}{2}=\cfrac{15C}{\pi }\implies 15\pi =30C \\\\\\ \cfrac{15\pi }{30}=C\implies \cfrac{\pi }{2}=C~\hfill \stackrel{\textit{horizontally to the right}}{-\cfrac{\pi }{2}=C} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=2cos\left(\frac{\pi }{15}x-\frac{\pi }{2} \right)~\hfill[/tex]
Check the picture below.
Elaina is planning to save enough money to buy laptop computer. She needs $600. She already has $200 in her bank account. She is planning to deposit $40 each week into her bank account. Write an equation to represent Elaina’s plan to save for a laptop computer based on X weeks.
Answer: 200+40x=600
Step-by-step explanation:
200+40x=600
600-200=400
40x=400
40/40= 1 or x
400/ 40=10
x=10
Please help meee I’m bad at math!!!!!
the answer to this question is C
y=2x+6×
Simplify the expression. Write your answer as a power.
2¹⁹×2⁵÷2¹²×2³
Answer:
32768^1
Step-by-step explanation:
Solved the equation and added the first power.
PLEASE HELP ME ASAPP !!
Answer:
1. you start with $ 3 and save $1 each month
2. your total savings is 3 times the number of month multiplied by itself
3. you save $3 the first month and then each month the amount triples
Step-by-step explanation:
1.
as y axis represents savings while x axis represents months
the statement "you start with $ 3 and save $1 each month"
is best described by the graph of straight line having slope of 1 and intercept of 3.
2. your total savings is 3 times the number of month multiplied by itself
= 3(x)(x)
= 3x^2
3. as y axis represents savings while x axis represents months
the statement "you save $3 the first month and then each month the amount triples" is best described by the exponential graph starting to rise from point (1,3) which means $3 save at 1 month.
!
A parabola can be represented by the equation y2 = –x. What are the coordinates of the focus and the equation of the directrix?
ANSWER
Focus:
[tex](- \frac{1}{4} ,0)[/tex]
Directrix:
[tex]x=\frac{1}{4} [/tex]
EXPLANATION
The given parabola has equation:
[tex] {y}^{2} = - x[/tex]
We compare this to the general equation,
[tex] {y}^{2} = - 4px[/tex]
Comparing the coefficient of x, we have:
-4p=-1
[tex]p = \frac{1}{4} [/tex]
The focus is (-p,0)
[tex](- \frac{1}{4} ,0)[/tex]
The equation of the directrix is
x=p
[tex]x = \frac{1}{4} [/tex]
Answer:
A
Step-by-step ex
only if youre lazy like me to read it, its A
find the sum of the geometric series 6Σ3i i=2
[tex]
\sum_{3}^{6}2=\sum_{0}^{3}2=2+2+2=\boxed{6}
[/tex]
Or did you mean:
[tex]
6\times\sum{3i}=6\times\sum{6}=6\times6=\boxed{36}[/tex]
The LCM of three numbers is 48. What are the numbers?
2, 3, 4
6, 16, 24
3, 8, 12
6, 8, 12
Answer:
{6, 16, 24}
Step-by-step explanation:
The least common multiple is the least number that is common to the multiples of two or more numbers.
The LCM of 2,3,4 is 12
The LCM of 6,16,and 24 is 48
The LCM of 3,8, 12 is 24.
The LCM of 6,8, 12 is 24.
The numbers that have the least common multiple of 48 is {6, 16, 24}
[tex]6=2\times 3[/tex]
[tex]16=2^4[/tex]
[tex]24=2^3\times 3[/tex]
The LCM is the product of the highest powers of the common factors
[tex]2^4\times3=48[/tex]
How much fencing would he need?
The width of the garden would be found by dividing the area by the length.
Width = 324 / 24 = 13.5 feet.
Now you need to find the total perimeter of the garden:
Perimeter = 2 x length + 2 x width
Perimeter = 2 x 24 + 2 x 13.5
Perimeter = 48 + 27
Perimeter = 75 feet.
He will need 75 feet of fence.
Answer:
75 feet of fence
Step-by-step explanation:
324/24=13.5
13.5+13.5+24+24=75
four friends were born on consecutive years the sum of their ages is 62 what is the youngest friend
Answer:
The age of youngest friend = 14 years
Step-by-step explanation:
It is given that, four friends were born on consecutive years the sum of their ages is 62
Let 'x' be the age of youngest friend
age of other friends are (x + 1), (x + 2) and (x + 3)
To find the age of youngest friend
From the given information we can write,
x + (x + 1) + (x + 2) + (x + 3) = 62
4x + 6 = 62
4x = 62 - 6 = 56
x = 56/4 = 14
Therefore age of youngest friend = 14
Which statement about the diagram are correct check all that apply
where is the picture for the problem?
Answer: here’s the possibile picture and answer
Step-by-step explanation:
(C & D)
Sydney needs 70cm of fringe for each scarf she make how many scarves can she make if she has 6 meters if Fringe
Answer:
Sydney can she make 8 scarves
Step-by-step explanation:
Remember that
1 m=100 cm
so
6 m=6*100=600 cm
using proportion
70/1=600/x
x=600/70
x=8.6 scarves
therefore
Round down
Sydney can she make 8 scarves
4% of 975 is what number
Answer:
39
Step-by-step explanation:
Answer:
4% of 975 is 39
Step-by-step explanation:
4% of 975 = 0.04 x 975 = 39
Answer
4% of 975 is 39
Y+2=-3(x-4)
Find the missing value in the solution to the equation. ( , -2)
Answer:
(4,-2)
Step-by-step explanation:
plug in and simplify;
y+2=-3(x-4)
-2+2=-3(x-4)
0=-3x+12
3x=12
x=4
The missing value in the solution of the equation is ( 4 , -2)
What is an Equation ?An equation is a mathematical statement that consists of two algebraic expression equated by an equal sign.
The given equation is
y +2 = -3 (x-4)
The value of x at y = -2 ,
Substituting the value of y in the equation
-2 + 2 = -3 ( x -4)
0 = -3x +12
-12 = -3x
x = 4
The value of x is 4
Therefore the missing value in the solution of the equation is ( 4 , -2)
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in need help ASAP!! 25 points!
Kami and her mother offer tours of a nearby canyon. They charge a $50 base rate plus $10 per person for a 2.5 hour tour. Which equation represents A, the amount they make to tour p people thorough the canyon?
A. 2.5p+50=10A
B. 10p+50=A
C. 2.5p=50=A
D. 10/p+50=A
Answer:
b
Step-by-step explanation:
becuase 10p which it states in the equation the 10 dollars per person and plus 50 base and 2.5 is not in the equation
Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6in. The height of the prism is 10in
ANSWER
[tex]211.2 {in}^{2} [/tex]
EXPLANATION
The surface area of a triangular prism is
equal to the area of two triangular faces
plus the area of the three rectangular faces.
The area of the equilateral triangle is calculated using the formula:
[tex] = 2 \times \frac{ \sqrt{3} }{4} {s}^{2} + 3 \times \: bh[/tex]
where s=6 is the length of one side.
and b=6 is the breadth of the rectangle and h=10 is the height of the rectangle.
Surface area
[tex]= 2 \times \frac{ \sqrt{3} }{4} \times {6}^{2} + 3 \times \: 6 \times 10[/tex]
[tex]= 18\sqrt{3} + 180[/tex]
=211.2square inches.