which expression can be used to calculate the rate per second at which the machine launches the balls? (5 points) a fraction 12 over 2 b fraction 2 over 12 c fraction 48 over 2 d fraction 2 over 48

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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If Uriel can crush 3 cans in 23 of a minute, Uriel crushes aluminum cans at a rate of 4.5 cans per minute.

The problem gives us information about the number of cans Uriel can crush and the time it takes him to do so. We want to find the rate at which he crushes the cans, which is a measure of how many cans he can crush per minute.

To find this rate, we use a proportion. A proportion is a statement that two ratios are equal. In this case, we can set up a proportion that relates the number of cans Uriel crushes to the time it takes him to do so, and the rate at which he crushes the cans:

3 cans / (2/3 min) = x cans / 1 min

Here, the first ratio is the number of cans Uriel can crush in 2/3 of a minute (which is the same as saying that he can crush 3 cans in 2/3 of a minute). The second ratio is the unknown rate at which Uriel crushes cans per minute.

To solve for the unknown rate, we use cross-multiplication. This involves multiplying both sides of the proportion by the same value in order to isolate the unknown variable on one side of the equation.

In this case, we can cross-multiply by the denominators of each ratio:

3 cans × 1 min = (2/3 min) × x cans

Simplifying the left-hand side, we get:

3 cans × 1 min = 3 cans/min

Simplifying the right-hand side, we get:

(2/3 min) × x cans = 2x/3 cans/min

Putting these together, we get the equation:

3 cans/min = (2x/3) cans/min

We can now solve for x by isolating it on one side of the equation. To do this, we can multiply both sides by 3/2:

(3/2) × 3 cans/min = x cans/min

Simplifying, we get:

4.5 cans/min = x cans/min

Therefore, Uriel crushes aluminum cans at a rate of 4.5 cans per minute.

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Answer: pay attention

Step-by-step explanation:

The equation which correctly shows the relationship between x, number of hours and y, the amount of money she makes is; y = 12x + 7.

It follows from the task content that the relationship between y and x is to be.

By comparison with the slope-intercept equation; y = mx + c.

Since, slope, m is the rate of change; m = 12$ per hour.

Also, the nonrefundable one-time fee for showing up represents the y-intercept, c.

Therefore, the required equation is;

y = 12x + 5.

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By simplifying the ratio and adding the fractions, we found that 1/7 of the beads are purple pyramids.

Ratios are used to compare two quantities or values. They are often expressed in the form of a fraction or as a percentage.

The given ratio of purple pyramids to yellow spheres is 1:6. This means that for every 1 purple pyramid, there are 6 yellow spheres. We can express this ratio as a fraction:

Purple pyramids : Yellow spheres = 1 : 6

This can be simplified by dividing both sides by 6:

1/6 Purple pyramids : 1 Yellow sphere = 1/6 : 1

Now, we can add the two fractions to get the total fraction of pyramids in the necklace:

1/6 + 1 = 7/6

This means that out of every 7 beads, 1 is a purple pyramid. We can express this as a fraction:

1/7 of the beads are purple pyramids.

So, the fraction of the beads that are pyramids is 1/7.

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Complete Question:

A necklace is made from purple pyramids and yellow spheres in a 1:6 ratio . What fraction of the beads are pyramids?

The exponential equation after solving gives -26.

Exponential equations are equations where the independent variable, x is in the exponent.

The given equation is,

[tex]5^{7x+5}[/tex] = [tex]125^{2x-7}[/tex]

We know that 125 = 5³

[tex]5^{7x+5}[/tex] = [tex]5^{3(2x-7)}[/tex]

The base in the both sides of the equation is 5.

So,

7x + 5 = 3(2x - 7)

7x + 5 = 6x - 21

7x - 6x = -21 - 5

x = -26

Hence the value of x is -26.

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Answers: Each twin is 11 years old. Barb is 33 years old

Work Shown:

x = age of each twin

3x = Barb's age

x+x+3x = 5x = total of their ages = 55

5x = 55

x = 55/5

x = 11

Each twin is 11 years old. Barb is 3x = 3*11 = 33 years old.

Check: twin1+twin2+barb = 11+11+33 = 55

The answers are confirmed.

Answer:

22

Step-by-step explanation:

x+35=56

56-35=22

x=22

The percent table is:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

The initial price of the Loungy chair was $400.

So, the initial price(P₀) = $400

The price of the chair has gone up by 20%

So, increase in price(r) = 20%

The final price will be calculated by using the formula:

                          P = P₀(1 + r/100) (where P is the final price)

                          P = 400(1 + 20/100)

                          P = 400(1 + 0.2)

                          P = 400 × 1.2

                          P = $480

Hence, the final price of the Loungy chair is $480

Percent table:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

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The required probability of loosing both the contracts with 61% chances of winning first contract and 74% chances of second contract is equal to 0.1014.

Probability of winning the first contract 'P(A)' = 61%

                                                                  = 0.61

Probability of winning the second contract 'P(B)' = 74%

                                                                       = 0.74

Probability of loosing both the contracts is

=  [ 1 - P(A) ] × [ 1 - P(B) ]

= [ 1 - 0.61 ]  × [ 1 - 0.74 ]

= 0.39 × 0.26

= 0.1014

Therefore, the probability of loosing both the contracts as per given contracts winning possibility is equal to 0.1014.

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Answer:

Equation: 4(x + 1.5) = 38

Ticket Cost: $8, or x = 8

Step-by-step explanation:

The processing fee for each ticket is $1.50, or 1.5. This applies to each ticket, meaning that the price of one ticket (or x) should be added to 1.5. x + 1.5 represents the sum of a ticket and the processing fee. Since there were 4 tickets purchased, x + 1.5 is multiplied 4 times. That results in 4(x + 1.5). Finally, the total amount of money spent was $38, so 4(x + 1.5) = 38.

4(x + 1.5) = 38

4x + 6 = 38

4x = 32

x = 8

Check:

4 * 8 = 32 (cost of 4 tickets)

4 * 1.5 = 6 (cost of 4 processing fees)

32 + 6 = 38 (4 tickets + 4 processing fees = total)

Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.

Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.

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In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

In order to determine how much a normal family of four should budget for food in 9 years, we must take inflation into consideration.

To account for inflation, we can use the formula below to determine the future worth of the current food expenditures:

Future value = Present value * (1 + inflation rate)^n

where:

Present value = $897.20/month

Inflation rate = 4% per year

n = number of years

When we substitute the specified values, we get:

Future value = $897.20 * [tex](1 + 0.04)^9[/tex]

= $897.20 * 1.3981

= $1254.77 (to two decimal places in rounding)

Therefore, In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

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The sampling distribution of p hat follows a normal distribution thus, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The most typical form of distribution assumed in technical stock market analysis and other statistical investigations is the normal distribution. The mean and the standard deviation are the two variables that make up the standard normal distribution.

The sampling distribution of p hat follows a normal distribution thus,

Mu Subscript p hat = p

Here, the value of p = 0.12

Hence, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.

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Answer:

A. Mu Subscript p hat = p = 0.12

Step-by-step explanation:

Answer:

here you go

Step-by-step explanation:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Emily places a 10-foot tall pole to support the guy wire. After placing the pole, Emily measures the distance from the stake to the pole to be 11 ft: She then measures the distance from the pole to the tower to be 23 ft: Find the length of the guy wire, to the nearest foot.

Answer: The simple interest will be 20%.

Step-by-step explanation:

we know the simple interest of borrowed amount is:

S.I.= (P x R x T)/100 ..... (i)

where P⇒ Principal amount

R⇒ rate of interest

T⇒ time

and

total Pays Back amount = Principal amount + S.I.

Hence S.I. = Pays Back amount - Principal amount

Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means

if Principal amount = P

then Pays Back amount = 2P ⇒ S.I.= P

Rate of Interest = R

and Time = 5 years

P= (P x R x 5)/100

R= 100/5

R = 20%

Therefore, the simple interest is 20% annually.

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Step-by-step explanation:

A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.

For example:

[tex] \sqrt{ {7}^{2} - 4(4)(3) } = \sqrt{49 - 48} = \sqrt{1} = 1[/tex]

Since root 1, is a perfect square, we will have rational roots.

B.

[tex] {b}^{2} - 4ac < 0[/tex]

[tex]49 - 16c < 0[/tex]

[tex] - 16c < - 49[/tex]

[tex]c > \frac{49}{16} [/tex]

If c is greater than 49/16, we will have no x intercepts.

The simplified value is [tex]\frac{7a^{8}+12 }{21a^{5}}[/tex].

What is a mathematical expression?

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is [tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}[/tex].

This can be simplified by cross-multiplying and adding.

[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{5}*a^{3}+4*3}{3*7a^{5}} \\=\frac{7a^{8}+12}{21a^{5}}[/tex].

Therefore the simplified value of the given expression is :

[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{8}+12 }{21a^{5}}[/tex]

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Probability of a successful call 0.3157 = 31.57%  

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

A probability is the number of desired outcomes divided by the number of total outcomes.

The odds of making a sale on a single call are 6 to 13.

This means that in 6+13 = 19 calls, 6 are successful.

What is the probability of a successful call?

p = 6/19 =

0.3157 = 31.57% probability of a successful call.

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Answer:

Step-by-step explanation:

a) As the function is a quadratic you could restrict the domain by taking only values either side of the line x = 3. This means the domain will be

a) 3<x<∞

Or

b) -∞<x<3

b) the graph is attached below.

c) The equation of the inverse of f(x) can be found by switching x and y:

X = (y-3)²

√x = y - 3

y = √x + 3

However this takes in positive and negative values of the square root function. So in order to restrict this, we can take the positive square root only.

Thus y = +√x + 3

Answer:

Midpoint M (2,5)

S (3,2)

R (x,y) {we will find values for x and y}

(x + 3) / 2 = 2 and (y + 2) /2 = 5

x + 3 = 4 and y + 2 = 10

x = 4-3 and y = 10-2

x = 1 and y = 8

Therefore, coordinates of R (1,8)

Answer D

Step-by-step explanation:

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function over the x-axis, shifting it left by 3 units, and down by 2 units.

To reflect a quadratic function over the x-axis, we need to multiply the function by -1. Let's assume that our original quadratic function is f(x).

After reflecting the function over the x-axis, we get the new function g(x) = -f(x).

To perform a horizontal shift left 3 units, we need to replace x with (x + 3) in the function g(x). This gives us the new function h(x) = g(x + 3) = -f(x + 3).

Finally, to shift the function down 2 units, we need to subtract 2 from the entire function h(x).

Note that the order of the transformations is important. We first reflect the function over the x-axis, then shift it horizontally, and finally shift it vertically.

Hence,

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function

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The crane's shadow is 45 meters long when the crane is 24 meters tall.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"

Let the shadow cast by the crane be x.

The triangle formed by the tower and by the crane are similar.

Using the rule of similar triangles we have:

16/24 = 30/x

16x = (30)(24)

x = 45

Hence, the crane's shadow is 45 meters long.

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The solutions of the system of equations are (-1, 2) and (3, -5)

Here we have a graph of a system of equations. The solutions are all the points where the graphs of the two equations intersect.

Here we can see two intersection points, thus, we have two solutions. We can see that the first intersection is at (-1, 2) and the second intersection is at (3, -5)

So these two are the solutions of the system of equations.

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Answer: Distributive property and Commutative property (of multiplication)

Step-by-step explanation:

From 1 to 2, the parentheses coefficient is multiplied out to the parentheses. This is called distribution.

From 2 to 3, the numbers in each multiplication are rearranged. This would be the commutative property of multiplication.

HOPE THIS HELPS _- MM

Answer:

[tex]the \: formula \: for \: v = \frac{s}{t} [/tex]

[tex]when \: t = 2.5 \: \: s = 225 \: \: v = 90[/tex]

It should be noted that the set of odd integers has the density property. The density property states that for every subset of the real numbers that contains an infinite number of points, the interior of that subset contains a non-empty open interval. This is true

The set of odd integers is a countable subset of the real numbers, meaning that it can be put into a one-to-one correspondence with the natural numbers. However, even though it is countable, it still has an infinite number of points.

Since the set of odd integers contains an infinite number of points, it must contain a non-empty open interval in its interior. To see this, consider the interval (2n-1, 2n+1) for any positive integer n. This interval contains the odd integer 2n and its endpoints are both odd integers, so it is completely contained in the set of odd integers.

Therefore, the set of odd integers has the density property and is a dense subset of the real numbers.

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