Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.54.54, point, 5 milliliters per second. After 171717 seconds, 148.5148.5148, point, 5 milliliters of slushy remained.

How much slushy was originally in the cup?

milliliters

How long did it take Mariana to drink all the slushy?

seconds

Answer:

Point form:

(18/11 , -8/11)

Equation form:

x=18/11 , y=-18/11

Answer: 1.1

Step-by-step explanation:

10 * .11 is 1.1

When multiplying decimals by ten you move the decimal place once to the right.

Answer:

1.1

Step-by-step explanation:

0.11 x 10 = 1.1

You are moving the decimal point over once (x 10).

1 task will complete in 12.5 minutes

The robot can complete 9.6 task in 1 hour

Given,

Number of task a robot can complete = 4

Time taken by robot = 5/6 of 1 hour

5/6 of 1 hour = 5/6 × 60 minutes

= 300/6

= 50 minutes

Then,

4 task takes 50 minutes

1 task = 50 minutes / 4 task

= 12.5 minutes

So,

1 task = 12.5 minutes

x task = 60 minutes

1 : 12.5 = x : 60

1/12.5 = x / 60

1*60 = 12.5*x

60 = 12.5x

x = 60/12.5 = 4.8

x= 4.8

Therefore,

The robot can complete 4.8 task in 1 hour

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The interest rate on loan is 5.25%.

What is principal amount?

The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.

What is simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is  I=P.r.t

Given, Principal amount=$125,000, time=10years, Interest=$65,625.

Let r be the rate of interest, on applying simplest interest formula

                                               I=P.r.t

Where P=principal amount, r=rate, t=time.

I=125,000 x r x10

65,625=125,000 x r x10

r=[tex]\frac{65,625}{125,000(10)}[/tex]

r=0.0525

r=5.25%

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Answer:

2 : 5 or 2/5

Step-by-step explanation:

The ratio is 40 : 100, which can simplify into 2 : 5.

Answer: Yes

Step-by-step explanation: Can this help , 81 ÷ 3 is 27 which is one of the factors in the 3 multiplications

P(AIB) can be read as "the probability that A occurs given that B has occured. This is true.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred in probability theory.

Conditional probability: p(A|B) is the likelihood of event A occurring if event B occurs. For example, if you drew a red card, what is the likelihood that it is a four (p(four|red))=2/26=1/13? So there are two fours out of the 26 red cards (given a red card), so 2/26=1/13.

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The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

The correct option is  (A)

Given,

In the question:

Kaisorn deposits $50. 00 onto her public transportation card.

It costs her $2. 50 per trip to ride the subway.

Thom deposits $40. 00 on his public transportation card.

It costs him $2. 00 per trip to ride the subway.

Now, According to the question:

x → represents  the number of trips

y → represents the amount remaining in each account

According to the given condition:

The system of equations represents their transportation costs is :

50 − 2. 5x = y

40 − 2x = y

Hence, The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}[/tex]

now, keeping in mind that perpendicular lines have negative reciprocal slopes

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}[/tex]

so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}[/tex]

Answer:

Step-by-step explanation:

F 3/8x 3/8y

The sequence of transformations applied to function f(x) to produce function r(x) is a reflection across the y-axis and dilation by a scale factor of 1/4.

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function f(x) = -x would be transformed to function r as follows:

f(x) = -(-x)

r(x) = x

By applying a dilation with a scale factor of 1/4 to function r, we have:

r(x) = (1/4 × x)    → r(x) = f(1/4x)

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After Ann start to translate the document in 2 days, they need more 4.4 days to complete the work.

A unit work would take Ann 10 days to complete, means each day Ann completes 1/10 work

She works for 2 days, hence the work done = 2 x 1/20 = 2/10

The remaining work = 1 - 2/10 = 8/10

Then Ben joins.

A unit work would take Ben 12 days to complete, means each day Ben completes 1/12 work.

Each day, both Ann and Ben will complete:

1/10 + 1/12 = 11/60 unit work

The remaining work = 8/10

Hence, if each day 11/60 work can be completed, to complete 8/10 work, they need:

8/10 : 11/60 = 48/11 = 4.4 days

Therefore we can conclude, after Ann works for 2 days, they need more 4.4 days to complete the work.

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Answer:

25

Step-by-step explanation:

6.3= 1 blanket

to find 4 blankets you multiply 6.3 by 4

6.3x4=25.2

to the nearest whole number

25

56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.

Given,

The mean of the population, μ = 15.1 kg

Standard deviation, σ = 2.2 kg

We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;

Here,

z score = x - μ / σ

The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.

x = 16.5

z score = x - μ / σ

z = (16.5 - 15.1) / 2.2  = 0.64

Z = 0.64 has a p-value of 0.7389.

x = 13

z score = x - μ / σ

z = (13 - 15.1) / 2.2 = -0.95

Z = -0.95 has a p-value of 0.1711.

0.7389 - 0.1711 = 0.5678.

0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

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The set of ordered pairs that represent dilation factor of 2 is

a. A' (2, 12) B' (12, 12) C' (2, 4)

Dilation is a method of transformation which uses a scale factor. The scale factor determines if the dilation is magnification or shrinking

|0 < r < 1| is shrinking

|r > 1| is magnification

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

From the graph the coordinates are read and following the given transformation rule we have

preimage                           image

A (1, 6)   → (1 * 2, 6 * 2) →   A' (2, 12)

B (6, 6)  → (6 * 2, 6 * 2) →    B' (12, 12)  

C (1, 2)  → (1 * 2, 2 * 2) →    C' (2, 4)

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Answer:

larger number = 3

smaller number = -1

Step-by-step explanation:

x = larger number

y = smaller number

x+y=2

8-2y=4x-2 ---> 10 = 4x+2y

10 = 4x+2y

5=2x+y

y = 5-2x

2x=5-y

x+5-2x = 2

-x+5=2

-x=-3

x=3

3+y=2

y=-1

In the game where average score was 40 , then Jim's score was 100 .

In the question ,

it is given that ,

the average score in the game was 40  .

and also given that the Jim's score was 5/2 of the average .

So ,  the Jim's score can be calculated using the equation .

Jim's score = (5/2) × (Average score of the game)

Substituting the value of average in the equation ,

we get,

Jim's Score = (5/2) × 40

= 5 × 20

= 100

Jim's score is 100 .

Therefore , The Jim's score in the game where average score was 40 is 100   .

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The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer

what is power with respect to probability?

Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.

Power = P[ rejecting a null hypothesis that is false.]

So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false

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Answer:

7, 7/1

Step-by-step explanation:

The ratio 7:49 can be simplified to 1:7.

To solve for v, isolate the variable by dividing each side by factors that don't contain the variable.

Solve for v.

Hope this helps!

Answer:

a) ln(Length), ln(Time)

c)log(Length), log(Time)

e)Length, Time²

Step-by-step explanation:

Answer:

the person above me is correct!

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

Answer 0,4

Answer:

(-5,-1)

Step-by-step explanation:

Start at the orginal.  This is (0,0), the middle of the graph.  From that point you move 5 spaces left.  That is the -5 in the answer.  Then from that point, you move one space down.  That is the -1 in the answer.

Answer:

565/0.666=848.348

Step-by-step explanation:

if you needed variables added to the equation then show a picture and I can answer it.

The value of  the function (f + g)(x) = [tex]x^{2}[/tex] -5x + 9

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

f(x) = - 2x + 4, g(x) = [tex]x^{2}[/tex] -3x + 5

(f+g)(x) = f(x) + g(x)

So by adding the two functions

(f + g)(x) = -2x + 4 + [tex]x^{2}[/tex] -3x + 5

(f + g)(x)  = [tex]x^{2}[/tex] -5x + 9

In conclusion, the value of [tex]x^{2}[/tex] -5x + 9

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The matching numbers are:

1) 0.0000225 = 2 x 10⁻⁵

2) 219,000 = 2 x 10⁵

3) 3,40,000 = 3 x 10⁶

4) 297,000 = 3 x 10⁵

5) 0.0000034 = 3 x 10⁻⁶

What are Exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

We have to match the following terms :

1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵

2) 219,000 =  2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵

3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶

4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵

5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶

Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶

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A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

What is inequality?

Inequality is a relationship between two expressions or values that is not equal to each other.

This inequality may be written in two ways:

(a) y < x - 2 + 1

   or

   y < x - 1

(b) y < -x +2 + 1

   or

    y < -x + 3

A graph of the inequality is shown below. The shaded region satisfies the inequality.

Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

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The positive value of Z is 2.17.

What do you mean by normal distribution?

A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction. Because of its flared appearance, a normal distribution's graphic representation is occasionally referred to as a bell curve. The specific shape may change depending on how the population is distributed, but the peak and curve are always symmetrical and in the centre.

The information can be represented in the standard normal curve below:

It is given that 97% of the standard normal curve lies between −z and z.

The area in between is 0.97 meaning that one side is (0.97)/2 = 0.485

In addition, the region not shaded is the level of significance represented by (1-0.97)/2 = 0.03/2 = 0.015

From the Z-Score table (0 to Z table), this probability corresponds to the Z value of Z= 2.17 and -2.17

Thus the positive value of Z is 2.17.

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