Answer:
Step-by-step explanation:
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Answer:
15.0 in
Step-by-step explanation:
You want the height of a cone with radius 8 in and slant height 17 in.
Pythagorean theoremThe right triangle shown in the figure has height h, base x = 8 in, and slant height y = 17 in. The Pythagorean theorem tells you the relationship between these side lengths:
x² +h² = y²
8² +h² = 17²
h² = 17² -8² = 289 -64 = 225
h = √225 = 15.0
The height of the cone is 15.0 inches.
__
Additional comment
A triple of 3 integers that form the sides of a right triangle is called a "Pythagorean triple." The triple in this problem is one of those: {8, 15, 17}. Other Pythagorean triples you will often see in algebra, trig, and geometry problems are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {9, 40, 41}. You will also see multiples of these, for example 3×{3, 4, 5} = {9, 12, 15}.
It can be worthwhile to remember some of these. For this problem, recognizing 8 and 17 as part of the triple {8, 15, 17} means you can write down the answer with no further work.
Surface area of Rectangular pyramid
The surface area of the rectangular pyramid is 75 m².
What is surface area?Surface area is the sum of all the surfaces on each side of a three-dimensional shape.
To calculate the surface area of the rectangular pyramid, we use the formula below
Formula:
S.A = 2lh+l²............................. Equation 1Where:
S.A = Surface area of the rectangular pyramidl = Length of the base of the pyramidh = Slope height of the pyramidFrom the question,
Given:
l = 5 mh = 5 mSubstitute these values into equaation 1
S.A = 2×5×5+5²S.A = 50+25S.A = 75 m²Learn more about Surface area here: https://brainly.com/question/1297098
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Which of the following are like radicals? Check all
of the boxes that apply.
3x√x²y
O -12x√√x³y
O-2x√xy³²
Ox√yx²
-x√x²y
O 2√xy
The like radicals are 3x√x²y and x√yx², and the answer is:
3x√x²y, -2x√xy³², x√yx², 2√xy
What is expression?An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. It does not have an equal sign and can be simplified or evaluated by applying the appropriate rules of arithmetic.
According to the given information:
The like radicals have the same radicand (expression under the radical sign) and the same index (the number outside the radical sign). Checking each expression:
3x√x²y: The radicand is x²y and the index is 2.-12x√√x³y: The expression can be simplified as -12x√(x√(x^2 * y)) = -12x√x³√y, which has a different index than the first expression, so it is not a like radical.-2x√xy³²: The radicand is xy³² and the index is 2.x√yx²: The expression can be simplified as x√(y*x²) = x√(x²y), which has the same radicand and index as the first expression, so it is a like radical.-x√x²y: The expression can be simplified as -x√(x²y) = -x|x|√y, which has a different coefficient and a different index than the first expression, so it is not a like radical.2√xy: The radicand is xy and the index is 2.Therefore, the like radicals are 3x√x²y and x√yx², and the answer is:
3x√x²y, -2x√xy³², x√yx², 2√xy
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Help me on the questions please and thank you.
The lateral surface area of the rectangular prism is 308 units² and the total surface area is 398 units²
What is the lateral and total surface area of the rectangular prismThe formula of lateral surface area of the rectangular prism is given as;
LSA = 2(l +b)h
l = length b = breath or widthh = heightsubstituting the values into the formula;
LSA = 2(5 + 9) * 11
LSA = 308 units²
The total surface area is given by
TSA = 2(lb + bh + lh)
TSA = 2[(5*9) + (9*11) + (11*5)
TSA = 398 units²
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Quadrillion ABCD is dilated to create 2 images, as shown
Quadrilateral ABCD can be dilated by a scale factor 1.25 to create a smaller image and by a scale factor 1.5 to create a bigger image.
How to calculate the scale factor of the given quadrilaterals?To calculate the scale factor of a given shape for its dilation or reduction, the formula that should be used is given as follows:
Scale factor = bigger dimension/smaller dimension.
To create a smaller image;
bigger dimension length AB = 22in
smaller dimension length AB = 17.6in
Scale factor = 22/17.6 = 1.25
To create a bigger image:
Bigger dimension length = 33in
Smaller dimension length = 22in
scale factor = 33/22 = 1.5
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Which line is represented by y=3/2x-3 ? A. B. C. D.
Answer:
B
Step-by-step explanation:
the equation y=3/2x-3 has a slope of 3/2 and a y intercept of -3
So, first find the graph(s) that have the y intercept of -3. The only options would be B and C.
Next, from the y-intercept of -3, go UP 3, and to the RIGHT 2 to find your next point. This eliminates option C for the slope. The slope of option C is 2/3, not 3/2.
So, option B is correct. Hope this helps ;)
Answer:
B
Step-by-step explanation:
y = mx + b
y = mx (slope) + b (y-intercept)
The y-intercept of y = 3/2x - 3 is -3, so the graph needs to have a point at (0, -3). The slope is 3/2, if you go up 3 times and to the right twice from the point (0, -3), it will point (2, 0).
Airplane tickets to Fairbanks Alaska, will cost $958 each. Airplane tickets to Vancouver but I will call $734. How much can a four members of the Harrison family save on airfare by vacationing in Vancouver?
A four members of the Harrison family save $896 on airfare by vacationing in Vancouver.
Here, the airplane tickets to Fairbanks Alaska will cost $958 each.
⇒ c₁ = $958
where c₁ represents the airfare to Fairbanks Alaska
and the airplane tickets to Vancouver Canada will cost $734.
⇒ c₂ = $734
Let us assume that s represents the amount of savings per ticket.
⇒ s = c₁ - c₂
⇒ s = 958 - 734
⇒ s = $224
Since there are four members in the family.
So using unitary method the total savings would be,
⇒ t = 4 × s
⇒ t = 4 × 224
⇒ t = $896
Therefore, the total savings = $896
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The complete question is:
Airplane tickets to Fairbanks Alaska will cost $958 each. Airplane tickets to Vancouver Canada will cost $734. How much can the four members of a Harrison family save on airfare by vacationing in Vancouver?
Consider the graph of a function, f(x), which represents the number of cars on a busy road x hours after midnight. What is the approximate average rate of change, in cars per hour, of the function from x=0 to x =12 ?
On average, the number of cars on the busy road increases by 25 cars per hour from midnight to 12:00pm
What is the average rate of change of the functionThe average rate of change of a function from x=a to x=b is given by the formula:
average rate of change = (f(b) - f(a)) / (b - a)
Using this formula, we can calculate the average rate of change of the function f(x) from x=0 to x=12 as follows:
average rate of change = (f(12) - f(0)) / (12 - 0)
Where
f(0) = 0 and f(12) = 300 -- from the graph
So, we have
Rate = (300 - 0) / 12
Rate = 25
Therefore, the approximate average rate of change of the function from x=0 to x=12 is 25 cars per hour.
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the hypothesis statement h: μ < 60 is an example of an alternative hypothesis in a one-tail test. is true or false
The hypothesis statement h: μ < 60 is an example of an alternative hypothesis in a one-tail test is true
Define hypothesisA hypothesis is a proposed explanation or prediction for an observation or phenomenon that is based on limited evidence or data. It is a tentative statement or idea that can be tested through further observation, experimentation, or data analysis. Hypotheses are often used in scientific research as a starting point to investigate a research question or problem.
The hypothesis statement "μ < 60" is an example of an alternative hypothesis in a one-tailed test.
In a one-tailed test, the alternative hypothesis is directional and states that the population parameter is either greater than or less than the null hypothesis value.
In this case, the alternative hypothesis states that the population mean is less than 60.
The null hypothesis, in contrast, is typically a statement of "no effect" or "no difference" and is often denoted by H0.
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Monte owns a bakery. He has four employees, who each earn a different hourly wage.
Which two quantities are needed to determine the total amount of money Monte paid his employees this month?
A. the hourly salary of each employee
B. the number of hours the bakery was open each day
C. the number of hours each employee worked this month
D. the number of customers who visited the bakery this week
E. the total number of hours the employees have worked this year
The two quantities needed to determine the total amount of money Monte paid his employees this month are:
A. the hourly salary of each employee
C. the number of hours each employee worked this month.
How the total salary for the month is determined?With four employees at the Monte Bakery, who earn a different hourly wages, to work out the total salary for the month, Monte needs to multiply the hourly wage of each employee by the total number of hours each worked.
Thus, in this mathematical operation, we first use multiplication and then add each individual employee's total salary to sum the total salary for the month.
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calculate the work done required to drag a stone if mass 30kg on the ground through a distance of 50m.(Take acceleration due to gravity = 10m/s²).
Answer: Work done= F.d
= 15000 J
Step-by-step explanation:
Work done= Force*distance
where
Force= mass*acceleration
mass=30kg, acceleration= 10 m/s^2, distance
=30*10
=300 N
then by formula of work done
Work done= F.d
= 300*50
=15000J
1. Find volume, show work round to 2 decimal places
*cylinder*
in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma
A figure which has a sphare and cylinder. The total height of figure is 102mm and the height of cylinder is 76mm. Find Volume and Surface Area of the figure
The volume of the figure is approximately 50101mm^3 and the surface area is approximately 8253mm^2.
The figure consists of a sphere and a cylinder. We can find the volume and surface area of the figure by calculating the volume and surface area of each component separately and adding them together.
The height of the cylinder is given as 76mm, which means the remaining height of the figure must be occupied by the sphere. Thus, the radius of the sphere can be calculated as half the difference between the total height of the figure and the height of the cylinder:
Radius of sphere = (102mm - 76mm)/2 = 13mm
Now we can calculate the volume and surface area of each component:
Volume of cylinder = πr^2h = π(13mm)^2(76mm) ≈ 40899mm^3
Surface area of cylinder = 2πrh + 2πr^2 = 2π(13mm)(76mm) + 2π(13mm)^2 ≈ 6128mm^2
Volume of sphere = (4/3)πr^3 = (4/3)π(13mm)^3 ≈ 9202mm^3
Surface area of sphere = 4πr^2 = 4π(13mm)^2 ≈ 2125mm^2
Finally, we can find the total volume and surface area of the figure by adding the values for the cylinder and sphere:
Total volume = Volume of cylinder + Volume of sphere ≈ 50101mm^3
Total surface area = Surface area of cylinder + Surface area of sphere ≈ 8253mm^2
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Line Segment BD and Line Segment CK are diameters of ⊙ A. Line Segment BP and Line Segment QP are tangents to ⊙ A. Find each of the following. Show your work.
11.) m∠ABP=_________
12.) m∠BAK=_________
13.) m∠AQP=_________
14.) m∠QAK=_________
15.) Measure of Arc BK=__________
16.) Measure of Arc BQ=__________
17.) m∠CAD=_________
18.) m∠CAB=_________
19.) Measure of Arc CB= __________
20.) m∠CDA=_________
The measure of angle ABP from the given circle is 90°.
From the given figure,
11) Measure of angle ABP is 90°.
12) Measure of angle BAK is 180°-(90°+25°)
= 180°-115°
= 65°
13) Measure of angle AQP is 90°.
14) Measure of angle QAK is 180°-(90°+25°) (Because ∠BPA=∠QPA=25°)
15) Measure of Arc BK = Measure of angle BAK = 65°
16) Measure of Arc BQ = Measure of angle BAQ = 65°×2
= 130°
17) m∠CAD=m∠BAK=65°
Therefore, the measure of angle ABP from the given circle is 90°.
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Question 6
Hannah has $14,975 in an IRA. If she deposits $3,000 this year and then increases those deposits by $750 each following year, what rate does she need to earn to reach $1,000,000 in twenty-five years?
Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years.
To determine the rate Hannah needs to earn to reach $1,000,000 in 25 years, we can use the future value formula for an annuity:
[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]
where:
FV = future value (in this case, $1,000,000)
Pmt = periodic payment (in this case, Hannah's annual contribution)
r = annual interest rate
n = number of periods (in this case, 25 years)
Hannah will deposit $3,000 this year and increase her deposits by $750 each following year. So her annual contributions will be:
Year 1: $3,000
Year 2: $3,750
Year 3: $4,500
...
Year 25: $21,750
To simplify the calculation, we can use the average annual contribution over the 25-year period, which is:
[tex][(3,000 + 21,750) / 2] = $12,375[/tex]
Now we can plug in the values into the formula and solve for r:
[tex]1,000,000 = 12,375 * [(1 + r)^25 - 1] / r[/tex]
Multiplying both sides by r and dividing both sides by 12,375, we get:
[tex]r x (1 + r)^25 = 120.75[/tex]
We can solve for r using trial and error, or using a financial calculator or spreadsheet. Using trial and error, we can try different interest rates until we find the one that makes the equation true. One possible method is to start with a reasonable guess, such as 6%, and adjust up or down until we get close to 120.75. After a few iterations, we find that:
r = 5.88%
Therefore, Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years, assuming she deposits $3,000 this year and increases those deposits by $750 each following year.
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Find the surface area. Round your answer to the nearest tenth if necessary. Just enter the number, not the unit.
The total surface area of the prism is 177.2 m².
What is the surface area of the prism?The total surface area of the prism is calculated by applying the formula for total surface area of prism.
S.A = bh + (s₁ + s₂ + s₃)L
where;
b is the base of the triangleh is the height of the triangles₁ is the first triangular faces₂ is the second triangular faces₃ is the third triangular faceL is the length of the prismThe surface area of the prism is calculated as;
S.A = 4 m (3 m) + (3.8 m + 4 m + 4 m) x 14 m
S.A = 177.2 m²
Thus, the surface area of the prism is calculated using the formula for surface of right prism.
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May you please go over step by step of how to do this
The missing lengths of a geometric system are listed below: AC = 114, BC = 96, BE = 3
How to determine missing lengths of two similar triangles
In this problem we find a geometric system formed by two similar triangles. Two triangles are similar if every pair of corresponding sides have the same proportion. Then, the system is described by this proportion formula:
AB / AC = AE / AD = BE / CD
18 / AC = 15 / 95 = BE / 19
Then,
18 / AC = 15 / 95
AC = 18 × (95 / 15)
AC = 114
15 / 95 = BE / 19
BE = 19 × (15 / 95)
BE = 3
Now, we determine the length of side BC:
BC = AC - AB
BC = 114 - 18
BC = 96
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44 friends evenly divided up an
�
n-slice pizza. One of the friends, Harris, ate
1
11 fewer slices than he received.
how many slices did he eat
The expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]
What is the expression for slices eaten?Let s be the number of slices each friend received.
Then the total number of slices on the pizza is n and we have: 44s = n because pizza was evenly divided among the 44 friends). Harris ate 11 fewer slices than he received, so he ate s - 11 slices.
The no of slices he received is s and we have:
s = (s - 11) + Harris's slices eaten
Substituting 44s = n, we will solve for s:
44s = n
s = n/44
So, the expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]
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Use the distributive property and inverse operations to solve the two-step equation.
-8(0.5x-3)=3
Answer:
5.25 or 5 1/4
Step-by-step explanation:
-8(0.5x-3)=3
first, just multiply -8 by 0.5x and -8 by -3 and you'll get:
-4x+24=3
next, subtract 24 on both sides, meaning subtract 24 by 24 on the left side and subtract 24 by 3 on the ride side:
-4x=-21
the final thing you have to do is divide -4 on both sides to get the x by itself:
x=5.25 or 5 1/4
A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9.5° (see figure). Find the change in elevation for a car descending the 4-mile stretch. (Round your answer to two decimal places.)
Step-by-step explanation:
We can use trigonometry to solve this problem. The grade of the road is given as an angle of 9.5°. This means that for every 1 unit of horizontal distance traveled, the elevation changes by the tangent of 9.5°.
We want to find the change in elevation for a car descending the 4-mile stretch. To do this, we can multiply the length of the road by the tangent of the grade angle:
Change in elevation = 4 miles x tan(9.5°)
Using a calculator, we can find that tan(9.5°) = 0.1664. Substituting this value into the equation, we get:
Change in elevation = 4 miles x 0.1664 ≈ 0.67 milesTo convert this to feet, we can multiply by the number of feet in a mile:
Change in elevation = 0.67 miles x 5,280 feet/mile ≈ 3,539 feetTherefore, the change in elevation for a car descending the 4-mile stretch is approximately 3,539 feet.
Question 3 out of 8:’sks
The picture below shows the graph of the inequality of x² ≤ 4
Option B is correct.
What is inequality in mathematics?In mathematics, an inequality is described as a relation which makes a non-equal comparison between two numbers or other mathematical expressions which is used most often to compare two numbers on the number line by their size.
A graph of inequality denotes that the variables is the set of points that represents all solutions to the inequality.
A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
Therefore, the correct option is B. x² ≤ 4
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PLEASE HELP ASAP‼️Solve the triangle MNO (find m
m and n).
n =
M
34°
12 cm
m=
N
4
If a reduced echelon matrix T(x) = 0 has a row of [ 0 . . 0 | 0] or [0 . . .0 | b] , where b =/= 0, it's considered one to one.
a. true
b. false
The correct answer is false. A reduced echelon matrix [tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where[tex]b \neq 0[/tex], is not considered one-to-one.
Let's first define what it means for a matrix to be one-to-one.
A matrix is said to be one-to-one if each column of the matrix is linearly independent.
This means that for any given input, there is only one possible output.
Now, let's consider the reduced echelon matrix T(x) = 0. If this matrix has a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], b ≠ 0, it means that one of the variables in the system of equations represented by the matrix is a free variable.
This free v[tex]T(x) = 0.[/tex]ariable can take on any value, and the other variables will adjust accordingly.
If the reduced echelon matrix is [tex][1 0 | 2; 0 0 | 0],[/tex] the system of equations would be [tex]x = 2[/tex] and y can be any value.
This means that the matrix is not one-to-one, because there are multiple outputs for the same input.
the correct answer is false.
A reduced echelon matrix[tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where [tex]b \neq 0[/tex], is not considered one-to-one.
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example of solving related rate problem:Water leaking onto the floor creates a circular pool with an area that increases at a rate of 3cm^2 / min. How fast is the radius of the pool changing at the moment when the radius is 10 cm?
The radius of the pool is changing at a rate of 3 / (20π) cm/min when the radius is 10 cm.
To solve this problem, we'll use the given information and the area formula for a circle.
Write the formula for the area of a circle:
[tex]A = \pi r^2[/tex],
where A is the area and r is the radius.
Differentiate both sides of the equation with respect to time (t): [tex]dA/dt = d(\pi r^2)/dt.[/tex]
Apply the chain rule on the right side: [tex]dA/dt = 2\pi r(dr/dt),[/tex]
where dr/dt is the rate of change of the radius.
Plug in the given values:
dA/dt = 3 cm²/min (given) and r = 10 cm (given at the moment of interest).
Solve for dr/dt:
3 = 2π(10)(dr/dt).
Isolate dr/dt:
dr/dt = 3 / (20π)
Simplify:
dr/dt = 1 / (20π/3) = 3 / (20π).
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what is true about the slope/derivative of a vertical tangent?
The slope and derivative of a vertical tangent are both undefined due to the vertical nature of the tangent line.
The slope/derivative of a vertical tangent.
A vertical tangent occurs when a curve has a point where its tangent line is vertical.
In terms of the slope and derivative, the following is true about the vertical tangent:
Slope:
The slope of a vertical tangent is undefined because the vertical line has no run (change in x). Slope is calculated as the rise (change in y) divided by the run (change in x), and division by zero is not possible.
Derivative:
The derivative of a function at a point represents the slope of the tangent line to the curve at that point.
When the tangent is vertical, the derivative is also undefined because the slope is undefined.
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2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
-5
N
The answer of the given question based on the rectangle is , The MNOP congruence is shown by Side-Angle-Side (SAS) and the steps are given below.
What is Diagonal?In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon or a polyhedron. In other words, a diagonal is a line segment that joins two corners or vertices of a shape that are not next to each other. For example, in a rectangle, the diagonals are the line segments that connect opposite corners of the rectangle.
To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following steps:
Draw the diagonal MO and the diagonal NP.Since MNOP is a rectangle, we know that angles M and N, as well as angles O and P, are right angles. Therefore, we have four right triangles: triangle MNO, triangle NOP, triangle OPM, and triangle PMN.Since each of these triangles shares side OP, we can use the Side-Angle-Side (SAS) congruence criterion to show that triangles MNO and OPM are congruent, and triangles NOP and PMN are congruent.Since these triangles are congruent, we know that their corresponding sides are congruent. In particular, we know that segment MP is congruent to segment NO.Since MO and NP intersect at point Q, we know that Q is the midpoint of both segments MO and NP. Therefore, the diagonals of rectangle MNOP bisect each other.Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent.
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The answer please thank uu
Answer:
1. is (18,4)
2. is (8,10)
3. (-9,-8)
4. (9,-8)
Step-by-step explanation:
i promise its right please give brainliest
a probability distribution of the claim sizes for an auto insurance policy is given in the table below: claim size 20 30 40 50 60 70 80 probability 0.10 0.10 0.10 0.20 0.15 0.10 0.25 what percentage of the claims are within one standard deviation of the mean claim size?
55% of the claims are within one standard deviation of the mean claim size.
To find the percentage of claims that are within one standard deviation of the mean claim size, we first need to calculate the mean and standard deviation of the distribution.
The mean claim size is:
u = (20 × 0.10) + (30 × 0.10) + (40 × 0.10) + (50 × 0.20) + (60 × 0.15) + (70 × 0.10) + (80 × 0.25) = 54
The variance can be calculated as follows:
s^2 = [[tex](20-54)^{2}[/tex] × 0.10] + [[tex](30-54)^{2}[/tex] × 0.10] + [[tex](40-54)^{2}[/tex] × 0.10] + [[tex](50-54)^{2}[/tex] × 0.20] + [[tex](60-54)^{2}[/tex] × 0.15] + [[tex](70-54)^{2}[/tex] × 0.10] + [[tex](80-54)^{2}[/tex] × 0.25] = 340
The standard deviation is the square root of the variance:
s = √340 ≈ 18.44
To find the percentage of claims that are within one standard deviation of the mean claim size, we need to find the range of claim sizes that fall within the interval (u - s, u + s).
(u - s) = 54 - 18.44 = 35.56
(u + s) = 54 + 18.44 = 72.44
We can see from the table that the claim sizes 40, 50, 60, and 70 fall within this range, and their probabilities add up to:
0.10 + 0.20 + 0.15 + 0.10 = 0.55
Therefore, 55 percentage of the claims are within one standard deviation of the mean claim size.
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A deck of standard playing cards holds 52 unique cards.
36 of these cards are numbered cards (numbered 2-9), 4
of these cards are aces, and 12 of these cards are face
cards (jack, queen, and king). If you play a card game and
draw half of the face cards, one ace, and one fourth of the
numbered cards, how many cards do you have? How
many of each card type of card do you have? Cite
evidence from the problem.
PLS HELP
The total number of cards drawn is 16 and As a result, we have the following:
6 face cards, Aces 1, 9 numbered cards
How to determine the type of each card?Because there are 12 face cards, half of them are 6 face cards.
There are 4 aces, so we draw 1.
There are 36 numbered cards in total, therefore one-fourth of them are 9 numbered cards.
We draw a total of 6 + 1 + 9 = 16 cards.
We may use the information provided in the problem to determine how many of each card type we have. We chose:
6 face cards make up half of the deck.
1 ace: 1 ace
9 numbered cards are one-fourth of the numbered cards.
As a result, we have:
6 face cards
Aces: 1
9 numbered cards
We can also ensure that the total number of cards drawn (16) corresponds to the number of cards in a regular deck by subtracting the cards we drew from the total number of cards: a deck of playing cards (52)
There are 52 - 16 = 36 cards left.
This means that there are 36 - 6 - 1 - 9 = 20 undrawn cards in the deck.
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Nathan is making lemonade to sell at a school fundraiser. His recipe requires $4 times as much water as sugar and twice as much sugar as lemon juice. He uses $3 cups of lemon juice. How many cups of water does he need
Nathan needs 24 cups of water to make his lemonade recipe.
Let's call the amount of lemon juice Nathan uses "x".
We know that Nathan uses 3 cups of lemon juice, so we can substitute x = 3 into the problem.
According to the recipe, the amount of sugar Nathan needs is twice the amount of lemon juice, so he needs 2x cups of sugar.
Substituting x = 3, we get that Nathan needs 2(3) = 6 cups of sugar.
The amount of water Nathan needs is four times the amount of sugar he needs, so he needs 4 times 6 cups of water, which is equal to 24 cups of water.
Therefore, Nathan needs 24 cups of water to make his lemonade recipe.
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