five times a number is 120

Answer:

-47

Step-by-step explanation:

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b^2−4 (ac)

Substitute in the values of a, b, and c.

1^2 − 4 (4 x 3)

Evaluate the result to find the discriminant.

Simplify each term.

One to any power is one.

1 − 4 (4 x 3)

Multiply

−4 (4 x 3)

Subtract 48 from 1.

-47

Answer:

2.0333

Step-by-step explanation:

log 108

Express 108 in terms of 2 & 3.

108 = 2 * 2 * 3 * 3 * 3 = 2² * 3³

log 108 = log 2² * 3³ = log 2² + log 3³ [Using Product Law]

= 2log 2 + 3log 3 [Using Power Law]

Now put the values of log 2 & log 3:

2log 2 + 3log 3

= 2*0.3010 + 3*0.4771

= 0.6020 + 1.4313

= 2.0333

If the difference between the water temperature and the room temperature is halved every 5 minutes, then the water temperature in degrees fahrenheit, after 15 minutes 86 f        

If a cup is boiling water (212 f) is placed to cool in a room whose temperature remains constant at 68 f. suppose the difference between the water temperature and the room temperature is halved every 5 minutes .

Temperature can be measured in degree celsius, degree fahrenheit and kelvin. so here the temperature measured in degree fahrenheit

Initially the difference between water and room temperature is,

212 - 68 = 144f                

For every 5 minutes the difference of water and room temperature is halved,

After 5 minutes the difference is, 144/2 = 72 f

After 10 minutes the difference is, 72/2 = 36 f

After 15 minutes the difference is, 36/2 = 18 f

So the water temperature in degrees fahrenheit, after 15 minutes will be the sum of room temperature and difference between the temperatures of water and room after 15 minutes and it is given as, 18 f + 68 f = 86 f

Therefore, the water temperature in degrees fahrenheit, after 15 minutes is 86 f.

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Answer:

d > - 7

Step-by-step explanation:

Swap the sides :

- 11.8d < 82.6

Then, divide both sides of the inequality by -11.8 and flip the inequality sign

Answer:

To solve it, you need to use vectors. Let me show you how.

To find the vector that describes the translation, we need to subtract the coordinates of point A from the coordinates of the translated point. Let the vector be v. Then we have:

v = (-1, -3) - (-4, 2)

v = (-1 + 4, -3 - 2)

v = (3, -5)

To write this vector as a column vector, we write it vertically with square brackets. So we have:

v = [3

   -5]

Therefore, the vector that describes the translation is [3

   -5].

Step-by-step explanation:

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Measures of variability include the range, variance, and standard deviation, and they give us a sense of how spread out the scores in a distribution are. These measures help us understand the variability or dispersion of the data and how far the individual scores in a distribution deviate from the mean or other measures of central tendency.

Measures of central tendency, such as the mean, median, and mode, describe the central or typical value of a set of scores. They provide a summary of the data and a single value that represents the center of the distribution.

The decisions regarding graph size, shape, and style are usually based on the type of data being presented and the message being conveyed. A histogram, for example, may be used to visually display the distribution of a set of scores, and the size, shape, and style of the graph can be adjusted to highlight important features of the data.

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The ways the system of equations 9x - 2y = 43x+8y=12can be solved are:

A) Multiply the first equation by 4, then add the equations.

D) Multiply the second equation by 3, then subtract the equations.

From the given equations,9x - 2y = 43x+8y=12we need to use wyas of solving simultaneous equation to solve it.

Then if we Multiply the first equation by 4,  thge we can then perform addition to the second equation like

9x - 2y = 4

36x - 8y = 4

3x+8y=12

then if we add to equation 2 we have

39x =12

then we can solve x = 12/39

The same can be done with equation D .

Therefore, option A and D are correct.

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Answer:

Step-by-step explanation:

To solve the system of equations:

9x - 2y = 4 ...(1)

3x + 8y = 12 ...(2)

We can use elimination method by adding or subtracting the equations in a way that one variable is eliminated.

Here are the possible ways to solve the system:

A) Multiply the first equation by 4, then add the equations.

Multiplying the first equation by 4 gives:

36x - 8y = 16

Adding the resulting equation to the second equation gives:

36x - 8y + 3x + 8y = 16 + 12

Simplifying the equation:

39x = 28

x = 28/39

Substituting x in equation (1) gives:

9(28/39) - 2y = 4

Solving for y gives:

y = -155/78

Therefore, the solution is (x,y) = (28/39, -155/78).

B) Multiply the second equation by 3, then add the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Adding the resulting equation to the first equation gives:

9x - 2y + 9x + 24y = 4 + 36

Simplifying the equation:

18x + 22y = 40

Dividing the equation by 2 gives:

9x + 11y = 20

Substituting 9x from equation (2) gives:

3x + 8y = 12

Solving for x gives:

x = (12 - 8y)/3

Substituting x in equation (3) gives:

9[(12-8y)/3] + 11y = 20

Solving for y gives:

y = 16/39

Substituting y in equation (2) gives:

3x + 8(16/39) = 12

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

C) Multiply the first equation by 3, then add the equations.

Multiplying the first equation by 3 gives:

27x - 6y = 12

Adding the resulting equation to the second equation gives:

27x - 6y + 3x + 8y = 12 + 12

Simplifying the equation:

30x = 24

x = 4/5

Substituting x in equation (1) gives:

9(4/5) - 2y = 4

Solving for y gives:

y = -23/10

Therefore, the solution is (x,y) = (4/5, -23/10).

D) Multiply the second equation by 3, then subtract the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Subtracting the second equation from the first equation gives:

6x - 26y = -8

Solving for x gives:

x = (26y - 8)/6

Substituting x in equation (2) gives:

3[(26y-8)/6] + 8y = 12

Solving for y gives:

y = 16/39

Substituting y in equation (1) gives:

9x - 2(16/39) = 4

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

The calculated test statistic (t = -0.527) is not less than -1.894 or greater than 1.894.

A hypothesis test can be performed to determine whether the mean volume of beverage in the cans differs from 12 ounces using the following steps:

(1)State the null hypothesis and the alternative hypothesis.

The null hypothesis is that the mean volume of beverage in the cans is equal to 12 ounces (μ = 12). The alternative hypothesis is that the mean volume of beverage in the cans is not equal to 12 ounces (μ ≠ 12).

(2)Select a level of significance (α).

In this case, the level of significance is α = 0.05.

(3)Calculate the sample mean and standard deviation.

The sample mean can be calculated as:

mean = (11.96 + 12.10 + 12.04 + 12.13 + 11.98 + 12.05 + 11.91 + 12.03) / 8 = 12.04375

The sample standard deviation can be calculated as:

[tex]s=\sqrt((11.96 - 12.04375)^2 + (12.10 - 12.04375)^2 + (12.04 - 12.04375)^2 + (12.13 - 12.04375)^2 + (11.98 - 12.04375)^2 + (12.05 - 12.04375)^2 + (11.91 - 12.04375)^2 + (12.03 - 12.04375)^2) / (8 - 1))[/tex] [tex]s=0.277764079[/tex]

(4)Calculate the test statistic.

The test statistic can be calculated as:

t = (mean - 12) / (s / sqrt(8))

(5)Determine the critical value(s) from the t-distribution table with 7 degrees of freedom (8 - 1).

At a significance level of 0.05 and 7 degrees of freedom, the critical value from the t-distribution table is approximately ±1.894.

(6)Compare the test statistic to the critical value(s).

If the test statistic is less than -1.894 or greater than 1.894, then the null hypothesis can be rejected. Otherwise, the null hypothesis cannot be rejected.

(7)Conclude the hypothesis test.

In this case, the calculated test statistic (t = -0.527) is not less than -1.894 or greater than 1.894. Therefore, we cannot reject the null hypothesis. This means that there is not enough evidence to conclude that the mean volume of beverage in the cans is different from 12 ounces.

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The value of the probability is 0.09

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

P(A) = 0.42, P(B) = 0.14, and P(A or B) = 0.47

Using the above as a guide, we have the following:

P(A and B) = P(A) + P(B) - P(A or B)

substitute the known values in the above equation, so, we have the following representation

P(A and B) = 0.14 + 0.42 - 0.47

Evaluate the expression

P(A and B) = 0.09

Hence, teh probability is 0.09

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Answer:

Step-by-step explanation:

200 rimwjh hdwqheywgygwuivug

The angle m∠B of the quadrilateral has a measure of 72°

The complete question is added as an attachment

For any quadrilateral, the sum of its four interior angles is equal to 360°,

Using the above as a guide, we have the following:

17x + 5 + 13x + 7 + 118° + 80° = 360°

Evaluate the like terms

So, we have

30x + 210° = 360°

Subtract 210° from both sides

30x = 150°

So, we have

x = 5

Given that

B = 13x + 7

We have

B = 13 * 5 + 7

Evaluate

B = 72

Therefore, the measure for the angle m∠B is 72°

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Answer:

18 cm

Step-by-step explanation:

Let's assume that the length of the stick is x cm.

Then, the lengths of pieces A, B and C would be 2x/10 cm, 3x/10 cm, and 5x/10 cm respectively.

Since C is longer than B by 8 cm, the length of C is 3x/10 + 8 cm, and the length of B is 3x/10 cm.

Therefore, the total length of the stick would be:

x = 2x/10 + 3x/10 + (3x/10 + 8)

x = 10x/10 + 8

x = 10 + 8

x = 18 cm

So, the length of the stick is 18 cm.

Answer: 20 cm

Step-by-step explanation:

create an equation.

2x : 3x : 5x

We are also told C is longer than B by 8 cm. So,

A : x : x+8

If 5x = x+8, solve for this: 4x = 8 so x =2.

Now, we can plug back in the original values.

2(2) + 3(2) + 5(2) = 20.

the stick is 20 centimeters long.

Answer:

  about 2.43 seconds

Step-by-step explanation:

You want the time when the height described by h = -16t² +36t +7 is equal to zero.

The quadratic equation ...

  -16t² +36t +7 = 0

can be solved using the quadratic formula. It tells you the solution to ...

  ax² +bx +c = 0 is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Then the solutions to the given quadratic are ...

  [tex]x = \dfrac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}=\dfrac{9\pm\sqrt{109}}{8}\approx\{-0.180,2.430\}[/tex]

The ball will hit the ground after about 2.43 seconds.

A sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.

To determine the required sample size for a 90% confidence interval with a margin of error of at most 0.04, we can use the formula:

[tex]n = \left(\frac{z \cdot \sigma}{E}\right)^2[/tex]

where:

n is the sample size

z is the z-score associated with the desired confidence level (90% confidence level corresponds to z = 1.645)

σ is the standard deviation of the population (unknown, so we use 0.5 as a conservative estimate, since the proportion of students who would patronize the nightclub is unknown and assumed to be 0.5 for maximum variability)

E is the maximum desired margin of error (0.04)

Plugging in the values, we get:

n = (1.645 * 0.5 / 0.04)²

n ≈ 424

Therefore, a sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.

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On solving the provided question, we can say that in a day, the expression will be  16*24 of 10.9% = 384 od 10.9% = 41.856

In mathematics, it is pοssible to multiply, divide, add, or remove. The construction of an expression is as follows: Expressiοn, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expressiοn (such as addition, subtraction, multiplicatiοn or division etc.) Expressions and phrases can be cοntrasted.

Any mathematical statement with variables, numbers, and an arithmetic οperation between them is called an expression or an algebraic expression. Fοr instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expressiοn, all of which are separated by the arithmetic sign +.

Dr. Drew cοnsumes 16 ounces of a caffeinated beverage first thing in the mοrning

Caffeine wears off at a rate of apprοximately 10.9% an hour.

in a day, the expression will be  16*24 of 10.9% = 384 od 10.9% = 41.856

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Answer:

213 ft^2

Step-by-step explanation:

In this problem, we can create a larger rectangle that engulfs this image with a few missing pieces on the corners. The area of that rectangle would be 18ft * 17 ft = 306 ft^2. The sum of the missing pieces is 2ft * 7ft + 5ft * 6 ft + 7ft * 7ft  = (14 + 30 + 49)ft^2 = 93 ft^2. So, the area of this figure is 306 - 93 = 213 ft^2

ANSWER: S=173ft^2

_._._._._._._._._._._._.

The properties of midpoints and rectangles to show that a quadrilateral with vertices at the midpoints of the sides of a rectangle is a rhombus.

In this problem, we will prove that a quadrilateral with vertices at the midpoints of the sides of a rectangle is a rhombus. This is an important result in geometry and is often used in solving more complex problems.

Let us consider a rectangle ABCD with sides AB, BC, CD, and DA. Let P, Q, R, and S be the midpoints of the sides AB, BC, CD, and DA, respectively.

We need to prove that PQRS is a rhombus, which means we need to show that all sides of PQRS are equal.

First, we can observe that PQ and SR are parallel to AD, and QR and PS are parallel to AB. This is because P and S are midpoints of AB and AD, and Q and R are midpoints of BC and CD, respectively. Therefore, PQ and SR are both half the length of AD, and QR and PS are both half the length of AB.

Next, we can use the fact that the opposite sides of a rectangle are equal. This means that AD = BC and AB = CD. Therefore, PQ and SR have the same length, as they are both half of AD. Similarly, QR and PS have the same length, as they are both half of AB.

Thus, we have shown that all sides of PQRS are equal, which means that PQRS is a rhombus.

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Complete Question:

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Answer:

OD 52020 cubic inches

Step-by-step explanation:

15.0×24.0=360

=360×8.5=3060

3060 inches×17 boxes=52020 inches

Therefore;52020 cubic inches storage space is needed for the crayons

Answer:12

16

20

44 these are the answers

Step-by-step explanation:

Answer:

4 more laps to reach the goal of 14.4 km.

Step-by-step explanation:

First, let's find the total distance covered so far: 720 m x 16 laps = 11,520 m.

Next, let's convert the goal distance to meters: 14.4 km x 1000 m/km = 14,400 m.

Finally, let's subtract the total distance covered from the goal distance to find the remaining distance: 14,400 m - 11,520 m = 2,880 m.

Since a lap is 720 m long, the remaining distance can be divided by 720 m to find the number of laps left: 2,880 m ÷ 720 m = 4 laps.

Therefore, the runner needs to run 4 more laps to reach the goal of 14.4 km.

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From The total mass of orange and box, the mass of oranges are 2kg and the mass of empty box is 23kg.

Let's use "o" to represent the mass of one orange and "a" to represent the mass of one apple.

We can set up two equations based on the information given:

Box + Oranges = 25 kg (equation 1)

Box + Apples = 11 kg (equation 2)

Oranges = 3 x Apples (equation 3)

We can substitute equation 3 into equation 1 to eliminate "oranges":

Box + 3a = 25 kg

We can substitute equation 3 into equation 2 to eliminate "oranges" again:

Box + a = 11/3 kg

Now we have two equations with two unknowns. We can solve for "Box" and "a" using either substitution or elimination. For example, we can multiply the second equation by 3 and subtract it from the first equation:

Box + 3a = 25

3(Box + a = 11)

-2Box + 2a = 2

Simplifying, we get:

Box - a = -1

We can add this equation to the second equation to get:

2Box = 11 - 1 = 10

So, Box = 5 kg.

Now we can substitute this value back into equation 2 to find "a":

5 + a = 11/3

a = 2/3 kg

Finally, we can use equation 3 to find the mass of the oranges:

Oranges = 3 x Apples = 3 x (2/3) = 2 kg.

Therefore, the mass of the oranges is 2 kg.

The mass of the empty box is the difference between the total mass of the box and the fruit and the mass of the fruit:

Mass of box = Total mass - Mass of fruit

From equation 1, we know that the total mass of the box and the oranges is 25 kg. From part a, we know that the mass of the oranges is 2 kg. Therefore:

Mass of box = 25 kg - 2 kg = 23 kg.

So, the mass of the empty box is 23 kg.

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____The given question is incomplete, the complete question is given below:

The total mass of a box and some oranges was 25kg . The total mass cii N the same box and some apples was 11kg . The mass of the oranges was 3 times the mass of the apples. (a) Find the mass of the oranges.. (b) Find the mass of the empty box.

Answer:

Step-by-step explanation:

I probalby am not reading the question correctly, but it seems be be asking the distance between Myrna's fingertip (18 feet above the ground!) and the top of the 27' foot flagploe.  We are not told where Myrna is standing, nor how she got her fingertip 18 feet high.  Since we are asked for a diagram, I did the best I could, not knowing much about Myrna other than she must be tall.  On her behalf, I assumed Myrna was directly under the flagpoe.  As shown in the attached diagram, her fingertip is 9 feet below the top of the flagpole.  

If the 24 foot wire is stretched all the way (i.e., it takes 24 feet to reach Myrna's fingertip), then she is not standing directly below the flagpole.   But this isn't clear in the problem.  In any event, if the question is how far she is from the very top of the flagpole from where she is standing, it would be the 24 foot lenght of the wire connecting her to the top of the flagpole.  If the question just wants the vertical distance, then it is 9 feet.

If she is standing away from the flagpole, then a diagram would appear roughly as follows:

 x

 x      s

 x 27'        s   24'

 x                       s

 x  ----------z--------------   y

 x                                   y

 x                                   y 18'

 x   ----------z--------------  y                  

flagpole                       Myrna

The distance z is calculated using the Pythagorean Theorem in the top triangle.  The left side is (27'-18') or 9'.  The hypotenuse is 24'.

  z^2 + 9^2 = 24^2

z = 22.2 feet.

The current age of Rita is 17 years and Cheryl is 7 years respectively, according to mentioned data.

Let us assume Rita's present age be x and Cheryl's age be y.

Rita's age two years ago = 3 × Cheryl's age two years ago

x - 2 = 3 (y - 2) - equation 1

Rita's age after three years = 3 × Cheryl's age after three years

x + 3 = 2 (y + 3) - equation 2

Solving equation 1

x - 2 = 3y - 6

x = 3y - 6 + 2

x = 3y - 4

Solving equation 2

x + 3 = 2y + 6

x = 2y + 6 - 3

x = 2y + 3

Keep the value of x from equation 2 in equation 1

2y + 3 = 3y - 4

Rearranging the equation

3y - 2y = 3 + 4

y = 7

Keep the value of y in equation x = 2y + 3

x = 2×7 + 3

x = 14 + 3

x = 17

So, Cheryl's and Rita's age is 7 and 17 years respectively.

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Step-by-step explanation:

solve like this.........

Answer:

a. 54 = 2 * 3³

b. 108 = 2² * 3³

c. 360 = 2² * 3² * 5

etc.

Step-by-step explanation:

So, you need to have a list of primes handy:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ...

Now, take your number and try to divide it by the first prime, 2.

54 = 27 * 2

That worked. Note down the 2 and repeat with the result. You find 27 cannot be divided by 2 again, but it can be divided by 3 (the next prime in the list):

27 = 9 * 3

Note down the 3 and repeat:

9 = 3 * 3

Note down a 3 again.

So you have

54 = 2*3*3*3 = 2 * 3³

You can continue this until the result is a prime number itself. Then you are done.

Answer: et's call the amount of strawberries Gill uses "x" grams. We know that the ratio of strawberries to bananas is 7:3, so we can set up an equation:

x/144 = 7/3

To solve for x, we'll multiply both sides of the equation by 144:

x = 7/3 * 144

x = 7 * 48

x = 336

So Gill uses 336 grams of strawberries in the smoothie.

Step-by-step explanation:

Melissa earned [tex]$152.84\\[/tex] this week. This means that she earned a total of [tex]$174.49[/tex] over the two week period.

To determine how much Melissa earned last week, we can subtract the [tex]$21.65[/tex] that she earned more this week from the total amount earned over the two week period. Therefore, Melissa earned [tex]$152.84[/tex] this week, and [tex]$21.65[/tex] more than she earned last week. Subtracting [tex]$21.65[/tex]from [tex]$174.49[/tex] gives us [tex]$152.84[/tex], which is the amount Melissa earned last week. This means that Melissa earned [tex]$152.84[/tex] last week .To summarize, Melissa earned $152.84 this week, which was[tex]$21.65[/tex] more than she earned last week. This means that Melissa earned a total of [tex]$174.49[/tex]over the two week period, and by subtracting [tex]$21.65[/tex] from the total amount earned over the two week period, we can determine that Melissa earned[tex]$152.84[/tex] last week.

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After solving the given inequality question, we will get  x < -9.

A mathematical sign for comparing two values or expressions is an inequality symbol. Inequality symbols include: (less than), > (greater than), (less than or equal to), and (greater than or equal to). Inequalities can be used to represent connections between two or more variables, for as 5 10 indicating that 5 is less than 10. Inequalities can also be used to define mathematical equations or to describe connections between variables. The equation x + 2 7 can, for example, be used to represent the relationship between x and 7, or to communicate that the value of x must be less than 5 for the equation to be true.

In the given question,

2/3x + 2y < -1/3x + 1

⇒ 2/3x + 2y - (-1/3x + 1) < 0

⇒ 5/3x + 3 < 0

⇒ 5/3x < -3

⇒ x < -9

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