Helen and Althea went shopping for towels to take to college. Helen bought 4 bath towels and 3 hand towels for $72 while Althea bought 3 bath towels and 6 hand towels of the same kind for $84.

Answers

Answer 1

Let b be the price of the bath towels and h be price of the hand towels. For Helen, we can write the following equation

$4b+3h=72$

And for Althea, we have

$3b+6h=84$

Then, we have 2 equations in 2 unknowns. By multipliying the first equation by -2, we have the following equivalent system of equation

$\begin{gathered} -8b-6h=-144 \\ 3b+6h=84 \end{gathered}$

By adding both equations, we have

$\begin{gathered} -5b+0=-60 \\ or \\ -5b=-60 \end{gathered}$

Then, b is given by

$\begin{gathered} b=\frac{-60}{-5} \\ b=12 \end{gathered}$

Therefore, 1 bath towel cost $12, which corresponds to option 3

Related Questions

(brainiest and 50 points)A data set is made up of these values.
1, 4, 5, 6, 6, 9, 11
Find the interquartile range.
A. 4 – 1 = 3

B. 11 – 9 = 2

C. 11 – 1 = 10

D. 9 – 4 = 5

Answers

Median of lower half (1,4,5) is 4Median of upper half(6,9,11) is 9

Interquartile range or IQR is difference of above medians

$\\ \tt\longmapsto 9-4=11$

Option D is correct

if the value stated by a null hypothesis is ______ the confidence interval, then the decision would have likely been to retain the null hypothesis.

Answers

If the value stated by a null hypothesis is within the confidence interval, then the decision would have likely been to retain the null hypothesis.

In hypothesis testing, the null hypothesis represents the default assumption or the claim that there is no significant difference or relationship between variables. The confidence interval, on the other hand, provides a range of plausible values for the population parameter based on sample data. If the value stated by the null hypothesis falls within the confidence interval, it means that the null hypothesis value is considered plausible or consistent with the observed data.

In this case, there is insufficient evidence to reject the null hypothesis, and the decision would be to retain it. On the other hand, if the null hypothesis value is outside the confidence interval, it suggests that the null hypothesis is unlikely, and the decision would be to reject it in favor of an alternative hypothesis.

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I’m trying to figure out #’s 31 and 32. I don’t need the answers I just need guidance on how to figure them out.

Answers

Answer:

open circle means less than OR greater to

closed circle means less than or equal to OR greater than or equal to

PLEASE HELP!!!
The function f(x) is shown on the graph.

The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.

What is the standard form of the equation of f(x)?

f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7

Answers

The standard form of the equation of f(x) is option a -x² - 6x + 7

Given,

The graph shows a downward open parabola.

The vertex points are:

(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)

Now,

We have to find the standard form of the function f(x):

As from the graph:

Parabola opens downward, so the function will be negative.

We have the options with:

a = -1, b = -6 and c = 7

Now,

Use x = -b/2a

x = 6/2 × -1 = 6/-2 = -3

Now,

f(x) = -x² - 6x + 7

f(-3) = -(-3)² - 6(-3) + 7

f(-3) = -9 + 18 + 7

f(-3) = 9 + 7

f(-3) = 16

That is, the points for the vertex in this equation is (-3, 16)

Then, the standard form of the equation of f(x) is option a -x² - 6x + 7

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Select the correct answer.
Which graph shows the solution region of this system of inequalities?
y ≥3(0.8)^x
y ≥ x² - 5

Answers

The solution to the inequality are the region in the shaded area and the graph is attached

How to determine the solution to the inequality

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

Answers

Answer:

Equation to be used: Point- Slope form $ y-y_1= m(x-x_1)$

y-intercept = - 12

Step-by-step explanation:

He should use point - slope form equation.

It is given that, line is passing through the points$ (1,\: -8) = (x_1\:y_1)$ and has a slope m = 4.

The equation of line in point-slope form is given as:

$y-y_1= m(x-x_1)\\y-(-8) = 4(x-1)\\y+8 = 4x - 4\\y = 4x - 4 -8\\\huge\red{\boxed{y= 4x - 12}}...(1)\\Equating\: equation\: (1) \: with;\\y = mx + b \\y-intercept\: (b) = -12$

Answer:

The answers are B and D.

Step-by-step explanation:

-2x-6y=8 and -6x-6y=0

Answers

Answer:

Assume we want to find the solution to this system of equations.

The solution is (2,-2)

Step-by-step explanation:

We can find the solution either mathematically or by graphing. I'll do both.

Math:

Rearrange:

-2x-6y=8

-6y=8 +2x

y = -(1/3)x -(4/3)

---

Now use this expression of y in the second equation:

-6x-6y=0

-6x-6(-(1/3)x -(4/3)) =0

-6x + 2x +8 =0

-4x = - 8

x = 2

---

Use x = 2 in the first equation to find y:

y = -(1/3)x -(4/3)

y = -(1/3)*(2) -(4/3)

y = -(2/3) -(4/3)

y = -(6/3) or -2

The solution is (2,-2)

===============

Graphing:

See attached graph.

Answer:

Step-by-step explanation:

-2x - 6y = 8

6x + 6y = 0

4x = 8

x = 2

-4 - 6y = 8

-6y = 12

y = -2

(2, -2)

Without multpilying tell which is greater 4/5 x 45 or 2/3 x 45. Explain

Answers

4/5 = 80%

2/3 = 66.66666...%

4/5 is a bigger fraction, so (4/5) x 45 is a bigger fraction.

Solve and check |2x − 1| = |4x + 9|

Answers

Answer:

x = -5 or x = -4/3

Step-by-step explanation:

First possibility.

|2x − 1| = |4x + 9|

2x - 1 = 4x + 9

2x - 4x = 9 + 1

-2x = 10

x = 10/-2

x = -5

Second possibility.

2x - 1 = - (4x+9)

2x - 1 = -4x - 9

2x + 4x = -9 + 1

6x = -8

x = -8/6

x = -4/3

Answer:

$ |2x - 1| = |4x + 9| $

this equation can be separated into 2 possible cases :

$2x - 1 = 4x + 9$

and

$2x - 1 = - (4x + 9)$

solve the 1st possible case:

$2x - 1 = 4x + 9$

$2x - 4x = 9 + 1$

$ - 2x = 10$

$x = - \frac{10}{2} $

$x = - 5$

solve the 2nd possible case:

$2x - 1 = - (4x + 9)$

$2x - 1 = - 4x - 9$

$2x + 4x = - 9 + 1$

$6x = - 8$

$x = \frac{ - 8}{6} $

$x = - \frac{4}{3} $

so the x value for this equation is:

x = -5 or x = -1.333

Please Help!! ASAP 50 POINTS!!!!!!!!

Answers

The statement will be m∠ABC = m∠GHI.

Reason: ∠ABC ≅ ∠GHI

Answer:

The statement will be m∠ABC = m∠GHI.

Step-by-step explanation:

Carefully examine a sample QM output below. Answer the questions that follow using the information provided in the table. Linear Programming Results X1 X2 X3 RHS Dual Maximize Const 1 Const 2 Const 3 Solution 15 20 16 5 6 4 210 0 10 8 5 200 2.27 4 2 5 170 0.93 0 5 32 612 Ranging Variable Original Value Lower Bound Upper Bound . Infinity Reduced 11.4 0 0 Value 15 20 16 26.4 25.6 50 0 X1 X2 X3 32 12.5 Dual value Original Lower Upper Bound CONSTRAINT Slack/Surplus ValueBound Dual value Original Lower Upper Value Bound Bound slack/Surplus Constraint 1 0 Constraint 2 2.27 Constraint 3 0.933 52 0 0 210 158 170 50 infinity 270.91 170 a. Construct the original LP problem from which the above output originated b. Show which constraints have slack/surplas and show how to compute the values c. What is the optimal solution? Using the information provided, show how the optimal solution is computed. otpede todia d. If the profit froit X2 increases to $24, what happens to the optimal solution? e. you change oncrease) the right-hand side of constraint 3 by 10unts, by how much would the proht increase as a result of this, L If you change freduce) the right-hand side of constraint 2 by 5 units, by how much woukd the profa decrease as a result of this? What is the higher bound on this What conclusions can you draw froem this regarding bounds of the right-hand-side vales and the dual price

Answers

The optimal solution is X1 = 15, X2 = 20, and X3 = 16. The profit can increase to $612 if the profit for X2 increases to $24. The profit will increase by $4 if the right-hand side of constraint 3 is increased by 10 units. The profit will decrease by $12.5 if the right-hand side of constraint 2 is decreased by 5 units, but the higher bound on this decrease is $0.

The original LP problem can be constructed by looking at the "Solution" and "Dual" rows of the table. The "Solution" row shows the values of the decision variables in the optimal solution. The "Dual" row shows the dual values of the constraints. The dual value of a constraint is the amount by which the objective function can increase if the constraint is relaxed by one unit.

The constraints with slack are constraints 1 and 3. These constraints are not binding in the optimal solution, which means that they could be relaxed without changing the value of the objective function. The slack for constraint 1 is 52, which means that 52 units of the resource represented by constraint 1 are unused in the optimal solution. The slack for constraint 3 is 50, which means that 50 units of the resource represented by constraint 3 are unused in the optimal solution.

The optimal solution is computed by setting the decision variables equal to the values in the "Solution" row and then solving the resulting system of equations. In this case, the system of equations is:

X1 + X2 + X3 = 210

4X1 + 2X2 = 200

2X1 + 5X3 = 170

Solving this system of equations yields X1 = 15, X2 = 20, and X3 = 16.

If the profit for X2 increases to $24, then the dual value of constraint 2 will increase to 4. This means that the objective function can increase by $4 if constraint 2 is relaxed by one unit. In other words, if we increase the right-hand side of constraint 2 by one unit, then the optimal solution will change and the profit will increase by $4.

If the right-hand side of constraint 3 is increased by 10 units, then the dual value of constraint 3 will increase by $10. This means that the objective function can increase by $10 if constraint 3 is relaxed by one unit. In other words, if we increase the right-hand side of constraint 3 by 10 units, then the optimal solution will not change and the profit will increase by $10.

If the right-hand side of constraint 2 is decreased by 5 units, then the dual value of constraint 2 will decrease by 2.5. This means that the objective function will decrease by $2.5 if constraint 2 is relaxed by one unit. However, the dual value of constraint 2 is also bounded below by 0. This means that the profit can only decrease by $2.5 if constraint 2 is relaxed by one unit.

In conclusion, the bounds of the right-hand-side values and the dual prices are related to the feasibility of the solutions. If the right-hand side value of a constraint is less than the dual price of that constraint, then the constraint is infeasible. If the right-hand side value of a constraint is equal to the dual price of that constraint, then the constraint is binding in the optimal solution. If the right-hand side value of a constraint is greater than the dual price of that constraint, then the constraint is not binding in the optimal solution.

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In basketball, hang time is the time that both of your feet are off the ground during a jump. The equation for hang time is t = 2 (StartFraction 2 h Over 32 EndFraction) Superscript one-half , where t is the time in seconds, and h is the height of the jump, in feet. Player 1 had a hang time of 0. 9 s. Player 2 had a hang time of 0. 8 s. To the nearest inch, how much higher did Player 1 jump than Player 2? in.

Answers

Player 1 jumps 0.68in higher than Player 2

Given the equation for hang time expressed as:

$t=2(2h/32)^{1/2}$

Square both sides of the equation to have:

$t^2 = 4(2h/32)\\t^2 = 8h/32\\t^2 = 0.25h\\h = \frac{t^2}{0.25}$

If the time of jump for player 1 is 0.9s, the height covered will be "

h = 0.9²/0.25

h = 0.81/0.25

h = 3.24 in

If the time of jump for player 2 is 0.8s, the height covereed will be "

h = 0.8²/0.25

h = 0.64/0.25

h = 2.56 in

Difference in height = 3.24in - 2.56in

Difference in height = 0.68in

Hence Player 1 jumps 0.68in higher than Player 2

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INSTRUCTIONS
Solve the division problems
Name

Answers

Answer:

Step-by-step explanation:

Do the divison! :D It's hard to write out on here, but you can find a lot of other online resources on how to do it, I reccomend Khan Academy.

A padlock has a four-fidget code that includes digits from 0 to 9, inclusive. What is the probability that the code does not consist of all odd digits if the same digit is not used more than once in the code? Option 1: 120 out of 5,040 Option 2: 120 out of 3,024 Option 3: 2,904 out of 3,024 Option 4: 4,920 out of 5,040

Answers

Answer:

option 4

Step-by-step explanation:

Probability = number of favourable outcomes / total number of possible outcomes

total number of codes with an all odd digit = 3 x 5 x 7 x 2 = 120

total number of possible outcomes = 10 x 9 x 8 x 7 = 5040

probability all digits are odd = 120 / 5040

probability that the code does not consist of all odd digits = 1 - probability all digits are odd

1 - 120 / 5040 = 4920 / 5040

will 5 star worth 76pts

Answers

Answer:

i can't see anything

Step-by-step explanation:

Find the distance d between 21 = (-7 - 6i) and Z2 = (-15 – 12i). Express your answer in exact terms and simplify, if needed.

Answers

Answer:

Step-by-step explanation:

The distance is equal to the modulus of Z1-Z2.

$Z_1 - Z_2 = -7 - 6i - (-15 - 12i) = 8 + 6i\\|8 + 6i| = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$

Calculate the perimeter of a circle of radius 140mm using the value of pie as 22/7

Answers

Answer:

880 mm

Step-by-step explanation:

Perimeter of circle = 2πr

= 2(22/7)(140)

=880 mm

The perimeter of circle is 880 mm.

It is given that radius(r) = 140mm

The perimeter of a circle is also known as circumference of circle.

Circumference (c) = 2$\pi \\$r

It is also given that we have to use the value of pie as 22/7

Now,

c = 2 × 140 ×22/7

c = 6160/7

c = 880 mm

The perimeter of circle is 880mm.

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QUICK!!!!!!!! PLSSS I NEED HELP!!!

Answers

Answer:

It's the 4th one

Step-by-step explanation:

I hate think through math it’s the 4th one though.

A cookie recipe calls for 2 cups of m&m's to make 12 cookies. How many cups of m&m's are needed to make 84 cookies

Answers

Answer:

14 cups of m&m's to make 84 cookies

Step-by-step explanation:

If it takes 2 cups of m&m's to make 12 cookies. then you need to see how many times the original recipe will go into 84. Seeing that 84/12=7 you would need to multiply the original recipe by 7.

For example:

84/12=7 This is how many times the recipe is multiplied if you make 84 cookies.

2x7 is the amount of m&m's you would need to make the larger batch of cookies.

Find the perimeter and area of the figure.
10 ft
3 ft
The perimeter of the figure is
feet.
47
The area of the figure is
square feet.
HELP ME PLEASE

Answers

Answer: the perimeter is 26 feet squared. the area is 30 feet

perimeter is all sides added together:

10+10+3+3= 26

area is base times length

10×3=30

dont forget units

calculate the coefficient of variation for a sample of cereal boxes with a mean weight of 340 grams and a standard deviation of 5.2 grams.? 0.15% A
1.53% B
15.29% C
0.65% D

Answers

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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A student found that the side lengths of a square rug were 1.80. The student was asked to
report the area using the correct number of significant digits. He wrote the area as 3.2.

Answers

The exact answer would be 3.24 but if you were asked to round, then yes he was right.

PLSSSSS HELP ILLLL GIVE U 100 POINTS

Answers

Answer:

8^3 = 512

8^2 = 64

8^1 = 8

8^0 = 0

Step-by-step explanation:

Hey there!

An exponent (a^2) is usually a number that is raised by a certain number that is expressed in whichever number you have raised times

Cell A.
8^4

= 8 * 8 * 8 * 8

= 64 * 64

= 4,096

Cell B.

8^3

= 8 * 8 * 8

= 64 * 8

= 512

Cell C.
8^2

= 8 * 8

= 64

Cell D.
8^1

= 8

Cell E.
8^0

= 1

Thus, your answers should be:

• 512
• 64
• 8
• 1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Plz help, I have to find the value each variable

Answers

answer:

・x = 50

・y = 61

step-by-step explanation:

・first things you should know —

y + 8 + 2x + 11 = 180 ( supplementary angles equal to 180° )

・five sides add up to 540° ( pentagon! )

・therefore:

108 + 125 + 98 + 98 + 2x + 11 = 540

440 + 2x = 540

2x = 100

・x = 50

use what you know and plug in ;

y + 8 + 2x + 11 = 180

y + 8 + 2(50) + 11 = 180

y + 119 = 180

・y = 61

・you can always plug in or substitute to check your answers.ᐟ

1. Use the number line to help you decide which statement is true.

Answers

It’s the last one because 1/2 is way more then 2/5 so I think it would be 1/5<1/2 so the last one

Answer:

2/5 < 1/2

Step-by-step explanation:

First, find the LCM for both denominators because you can't multiply 2 to get to 5. The LCM of 5 and 2 are 10, so you put that as their denominator. Then you have to think what you multiplied by 5 or 2 to get 10. For 2/5, you multiplied 5 by 2 to get 10, so multiply the numerator by 2 too. For 1/2, you multiplied 2 by 5 to get 10, so multiply the numerator by 5. Now, you will have 4/10 and 5/10. It's pretty obvious that 5/10 is bigger than 4/10, so the correct answer is 2/5 < 1/2

If triangle ABC is isosceles triangle in triangle DBE is an equilateral angle find each missing measure

Answers

The missing measuresSolution:Triangle ABC is isosceles.$∠DBC = y = 60° - 30° = 30° and ∠ACB = 120° - x = 30°.$ Therefore, Solving equations (7) and (8),$∠BAD = 30° and x = 90°$

Therefore, its base angles are equal.i.e.,$∠ABC = ∠ACB....(1)In triangle DBE, ∠BED = 60°$(Given).Also, we know that the sum of angles in a triangle is 180°.

, substituting in equation (3),$∠BDC = 180° - y - ∠ACB....(4)$

Now, in triangle $ABE, ∠ABE + ∠BAE + ∠BEA = 180°As ∠BAE = ∠BCD and ∠ABE = x,$

substituting in the above equation, $x + ∠BCD + 60° = 180°x + ∠ACB + 60° = 180° (As ∠BCD = ∠ACB)∠ACB = (180° - x - 60°) = 120° - x ....(5)$

Again, in triangle ADE, $∠ADE + ∠DAE + ∠EDA = 180°As ∠ADE = ∠ADB and ∠DAE = ∠ABE - ∠BAD (i.e., x - ∠BAD)and ∠EDA = ∠BED = 60°, substituting in the above equation,x - ∠BAD + ∠ABE - ∠BAD + 60° = 180°2x - 2∠BAD = 120°∠BAD - x = -60°$...........(8)Solving equations (7) and (8),$∠BAD = 30° and x = 90°$

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Given the following linear function sketch the graph of the function and find the domain and range. f (x) = -25 x + 4

Answers

Answer:

y=2/7x-2

Step-by-step explanation:

Use a table to find (3k−1)(4k+9).

Answers

Answer:

12k^2+23k-9

Step-by-step explanation:

(5n+ 5.82) + (2.29n+7.67) = (5n+______) + (5.82 +____

Answers

Answer:

(5n + 2.29n) + (5.82 + 7.67)

Step-by-step explanation:

Find sin X.
a. sin X= 4/5
b. sin X= 3/4
c. sin X= 3/5
d. sin X= 5/4

Answers

Answer:

sin X = 4/5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin X = opp side/ hypotenuse

sin X = 36/45

= 4/5

Let's find the value of sin X,

→ opp/hyp

→ 36/45

→ 4/5

The required answer will be,

→ a. sin X= 4/5

So, option (a) is the answer.

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