Simplify the ratio 28 pencils :16 Erasers.

An equation is formed of two equal expressions. The number of weeks for which Jamison needs to deliver papers to earn enough money for a bike is 24.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Jamison needs a total of $395 to buy a new bike but he has only $35 saved. Also, He earns $15 each week delivering newspapers.

Now, the equation that can represent the situation can be written as,

Cost of the bike = Amount Saved + Earning by delivering newspapers

Substituting the values,

$395 = $35 + $15x

where x is the number of weeks for Which Jamison needs to work in order to purchase the new bike. Therefore, solving the equation for x,

395 = 35 + 15x

395 - 35 = 15x

360 = 15x

x = 360 / 15

x = 24

Hence, the number of weeks for which Jamison needs to deliver papers to earn enough money for a bike is 24.

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Given info: -17/2 < (-1/2) - 4x ≤ 15/2

Find the value of x ?

Explanation:↓

Given in-equation is -17/2 < (-1/2) - 4x ≤ 15/2

⇛ -17/2 < (-1-8x)/2 ≤ 15/2

On multiplying with 2 then

⇛ 2(-17/2) < 2(-1-8x)/2 ≤ 2(15/2)

⇛ -17 < -1-8x ≤ 15

On adding 1 in the in-equation then

⇛ -17+1 < -1-8x+1 ≤ 15+1

⇛ -16 < -8x ≤ 16

On dividing by 8 in the in-equation then

⇛ -16/8 < -8x/8 ≤ 16/8

⇛ -2 < -x ≤ 2

⇛ 2 > x ≥ - 2

⇛ -2 ≤ x < 2

⇛ x € [-2,2)

Answer:→The solution set = { x : -2 ≤ x < 2, x€R }

The possible values of x = -2,-1,0,1

If you have any doubt, then you can ask me in the comments.

Answer:

third option

Step-by-step explanation:

using the rule of exponents

\((a^m)^{n}\) = \(a^{mn}\)

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

\(a^{\frac{m}{n} }\) = \((\sqrt[n]{a})^m\)

given

\((125x^{\frac{7}{3} }) ^{-\frac{1}{3} }\)

= \(125^{-\frac{1}{3} }\) × \(x^{-\frac{7}{9} }\)

= \(\frac{1}{125^{\frac{1}{3} } }\) × \(\frac{1}{x^{\frac{7}{9} } }\)

= \(\frac{1}{\sqrt[3]{125} }\) × \(\frac{1}{x^{\frac{7}{9} } }\)

= \(\frac{1}{5}\) × \(\frac{1}{x^{\frac{7}{9} } }\)

= \(\frac{1}{5x^{\frac{7}{9} } }\)

Answer:

The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.

Step-by-step explanation:

The Pythagorean Theorem

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

                                                     \(a^2+b^2=c^2\)

Applying the Pythagorean Theorem  to find the lengths of the three sides we get:

\((x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0\)

Solve with the quadratic formula

\(\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\)

\(x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

\(\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}\)

Because a length can only be positive, the only solution is

\(x=5+3\sqrt{10}\approx 14.5\)

The length of the short side is 14.5, the length of the other short side is \(14.5+4=18.5\), and the length of the longest side is \(14.5+9=23.5\).

Probability of (a) George winning is 0.1

                       (b) Julia winning is 0.05

Given in question,

Total ticket sold = 100

George bought tickets = 10

Julia bought tickets = 5

Winning ticket = 1

Selecting 1 ticket from 100 = \(\left[\begin{array}{ccc}100\\1\\\end{array}\right]\)

                                            = 100

Selecting 1 ticket from 10 = \(\left[\begin{array}{ccc}10\\1\\\end{array}\right]\)

                                         = 10

Selecting 1 ticket from 5 = \(\left[\begin{array}{ccc}5\\1\\\end{array}\right]\)

                                        = 5

Probability = favorable outcome/total outcome

Probability of George winning = \(\frac{10}{100}\)

                                                  = 0.1

Probability of Julia winning = \(\frac{5}{100}\)

                                             = 0.05

Hence, probabilities are 0.1 and 0.05 respectively.

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Answer: B. Two billion, eighty million :)

Answer:

$3792.69

Step-by-step explanation:

First, we would find the area,

Area = width x length

Area = 9 x 11

Area = 99\(m^{2}\)

Since each square meter costs $38.31, we would multiply the cost with the area,

Total Cost = 99 x 38.31

Total Cost = $3792.69

(Anyone can correct me if I'm wrong)

Answer:

35

Step-by-step explanation:

To make the expression If a = b + c and c ___ 0, then a > b  right, c will be c > 0.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /, and ^) that represents a quantity or a relationship between quantities. It can be  number, variable, or combination of both.

Expressions are used to represent mathematical operations, formulas, and relationships. They can be simple or complex, and they can be evaluated or simplified using mathematical rules and operations.

Now,

The correct relationship symbol that makes the statement true is ">" (greater than).

If a = b + c and c > 0, then a will always be greater than b. This is because adding a positive value (c) to b will increase the result (a) above the value of b.

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Answer: C

Step-by-step explanation:

Answer:

The correct option is (A).

Step-by-step explanation:

The complete question is:

A staff member at UF's Wellness Center is interested in seeing if a new stress reduction program will lower employees systolic blood pressure levels. Twenty people are selected and have their blood pressure measured. Each person then participates in the stress reduction program. One month after the stress reduction program, the systolic blood pressure levels of the employees were measured again. Did the program reduce the average systolic blood pressure level? Note: Differences were taken by taking "before systolic blood pressure" minus "After blood pressure"

The 95% confidence interval was (5.6, 10.2).

A. On average, the blood pressure levels before the stress reduction program were significantly higher than the systolic blood pressure levels after the stress reduction program, at the 95% confidence level

B. We are 95% confident that there is no difference in average systolic blood pressure levels before and after the stress reduction program.

C. On average, the systolic blood pressure levels after the stress reduction program were significantly higher than the systolic blood pressure levels before the stress reduction program, at the 95% confidence level.

Solution:

The hypothesis to determine whether the program reduced the average systolic blood pressure level, is as follows:

H₀: The program did not reduced the average systolic blood pressure level, i.e. d = 0.

Hₐ: The program reduced the average systolic blood pressure level, i.e. d ≠ 0.

A 95% confidence interval can be used to make conclusion for a hypothesis test.

If the 95% confidence interval consists of the null value, i.e. 0 then the null hypothesis will not be rejected. And if the confidence interval does not consists of the null value, the null hypothesis will be rejected.

The 95% confidence interval for the difference between the two data is:

(5.6, 10.2)

The 95% confidence interval does not consist of 0, the null value. And since all the values in the 95% confidence interval  are positive it clearly indicates that the program did not reduced the average systolic blood pressure level.

Conclusion:

On average, the blood pressure levels before the stress reduction program were significantly higher than the systolic blood pressure levels after the stress reduction program, at the 95% confidence level

Thus, the correct option is (A).

Answer:

See below

Step-by-step explanation:

Only 'improper' fractions would have this result....that is fractions with numerator  >  denominator

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

8.5 minutes

Step-by-step explanation:

the bottle will have leaked half into the 2nd bottle, meaning the 2nd bottle has half too

It will take 17 minutes for the two bottles to have the same amount of water.

Something calculated for one is called unit rate.

Given that, A full 17 oz bottle of spring water is leaking half of an ounce a minute into an empty bottle.

To have same amount of water both the bottles will have 17/2 = 8.5 ounces of water in them,

Since, it takes a minute to leak or fill half of an ounce,

Therefore, one ounce will take 2 minutes.

Therefore, 8.5 ounces will take = 8.5×2 = 17

Hence, it will take 17 minutes for the two bottles to have the same amount of water.

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Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

Answer:

k = 1

Step-by-step explanation:

Discriminant

\(b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0\)

\(\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}\)

\(\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}\)

\(\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}\)

As we need to determine the value of k that will give one solution, set the discriminant to zero.

Given equation:

\(y=kx^2-4x+4\)

Therefore:

Substitute these values into the discriminant and solve for k:

\(\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}\)

Answer:

For this question, you can use the simultaneous equation to solve this problem.

Equation 1 reads: x + y = 34. (There are 34 notes in total.)

Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)

To find x in terms of y, we can apply equation 1:

x = 34 - y

When we use this expression to replace x in equation 2, we obtain:

5(34 - y) + 10y = 235

By condensing and figuring out y, we get at:

y = 15

There are 15 $10 bills in the wallet as a result.

The equations that could be used to solve for the number of male runners (m) in the race are (m+75)/m = 3 / 2 and 150 + 2m = 3m. The correct options are A and B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that at a running race, the ratio of female runners to male runners is 3 to 2. There are 75 more female runners than male runners.

The ratio is written as,

f/ m = 3 / 2

There are 75 more female runners than male runners.

f = m + 75

The equation can be written as,

f / m = 3 / 2

( m + 75 ) / m = 3 / 2

Or

150 + 2m = 3m

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\( \frac{1}{ {3}^{3} } \)

Answer:

do 24 points i know it very well

Answer:

6 teaspoons of baking powder

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

sdfg

Step-by-step explanation:

jh

Answer:

Given: P.E=6.0J Height (h)= 3m g=9.8m/s^2

mass=?

Formula: P.E=mgh

m=P.E/gh

Application: To find mass of an apple

Answer+unit= 0.2 kg

Step-by-step explanation:

m=P.E/gh

= 6kgm^2/s^2 ÷ 9.8m/s^2*3m

=0.2kg

Answer:

Step-by-step explanation:

4^(4-7+1) = 4^-2

Answer: 4⁻²

Step-by-step explanation:

Use the power rule to combine exponents

4⁴ ⁻⁷ · 4

Subtract 7 from 4.

4⁻³ · 4

Multiply 4⁻³ by 4 by adding the exponents.

4⁻³ ⁺¹

Add -3 and 1

4⁻² is the answer

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

The final inequality is x > - 1.

Option D is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

√(x + 2) > -1

Squaring both sides.

x + 2 > (-1)²

x + 2 > 1

Subtracting 2 on both sides.

x > 1 - 2

x > -1

Thus,

x > - 1 is the final inequality.

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