Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?

Answer:

8.31

Step-by-step explanation:

-6n² = -414

[take away negative]

6n² = 414

[divide by 6]

n² = 69

n = 8.3066 (to 5 significant figures)

n = 8.31 (to 3 significant figures)

The probability of not rolling a 5 is [tex]\frac{1}{6}[/tex]

For any event A, the probability of not getting A is given by

[tex]P(not A)= 1- P(A)[/tex]

A number cube with six sides numbered 1 through 6 is rolled.

Then we have,

The total number of possible outcomes [tex]= 6[/tex]

Also, it is given that, The probability of rolling a 5 is

P(rolling 5)=[tex]\frac{1}{6}[/tex].

Now, the probability of not rolling a 5 will be

[tex]P(\text{not rolling a 5})= 1- P(\text{rolling 5})[/tex]

[tex]=1-\frac{1}{6}[/tex]

[tex]=\frac{5}{6}[/tex]

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Answer:

[tex]\huge\boxed{\sf m = 11}[/tex]

Step-by-step explanation:

-7m + 10m - 8 = 25

3m - 8 = 25

Add 8 to both sides

3m = 25 + 8

3m = 33

Divide 3 to both sides

m = 33/3

m = 11

[tex]\rule[225]{225}{2}[/tex]

No , Sydney does not have enough beads to make 15 rings .

beads required for one ring = 60

total rings she have to make is = 15

total beads she has to make rings = 852 beads

now,

60 beads make ring = 1

852 beads make rings = 1/60 x 852

                                     =    14.2 rings

                             OR

                          14 total rings

So , Sydney does not have enough beads to make 15 rings . she can only make 14 beads from the given amount of beads.

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What is the correct standard form for 400+3+0.07+0.001

403.071

Answer:

=4.03071×10²

Step-by-step explanation:

400+3=403

=403+0.07=403.07

=403.07+0.001=403.071

so 403.071 to standard form is 403.071 divide by 100 is 4.03071 and 10 and and also change to 2 zeros and Chang it to powers so =4.03071×10²

The sequence that can be defined by the recursive formula is (c) 4, 2.75, 1.5...

The function definition is given as

f(1) = 4

f(n + 1) = f(n) - 1.25 for n ≥ 1

Set n = 1

So, we have the following representation

f(1 + 1) = f(1) - 1.25

This gives

f(2) = f(1) - 1.25

So, we have

f(2) = 4 - 1.25 = 2.75

Set n = 2

So, we have the following representation

f(2 + 1) = f(2) - 1.25

This gives

f(3) = f(2) - 1.25

So, we have

f(3) = 2.75 - 1.25 = 1.5

So, we have

4, 2.75, 1.5...

The sequence that matches 2.75, 1.5... in the options is (c) 4, 2.75, 1.5...

Hence, the sequence is (c) 4, 2.75, 1.5...

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Answer:

C

Step-by-step explanation:

Because i got it right

The value of b of the equation is -9/5

Given that: line JK passes through points J(-4,-5) and K(-6,3) and if the equation of the line is written in slope-intercept form, y=mx+b

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

Using the y-y₁/y₂-y₁ = x-x₁/x₂-x₁

where (x₁, y₁) = (-4,-5) and (x₂, y₂) = (-6,3), the equation is:

y-(-5) / 3-(-5) = x-(-4)/-6-(-4)

y+5 / 3+5 = x+4 /6+4

(y+5)/8 =  (x+4)/10       cross multiply:

10(y+5) = 8(x+4)

10y + 50 = 8x + 32

10y = 8x +32 - 50

10y = 8x - 18

y = 8x/10 - 18/10

y = 4x/5 - 9/5

Comparing y = 4x/5 - 9/5 with y=mx+b

b = -9/5

Therefore, the value of b is -9/5

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The scenario describes the stratified random sampling method .

There are many sampling techniques to collect sample from a given population such as Simple random sampling , Systematic Sampling , Cluster Sampling and so on . All of them vary in reliability , accuracy and efficiency .

Stratified Random Sampling : It is a method of  sampling in which division of population is done into smaller subgroups known as strata .The strata are formed based on member's shared attributes or characteristics . It has numerous applications . It is also called proportional random sampling or quota random sampling .

Therefore , the scenario describes the stratified random sampling method .

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The members who have registered for both batting and fielding are 306.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

Total members = 850

Number of members registered for batting = 80%

Number of members registered for fielding = 56%

Members who participated in both,

80% of 850 + 56% of 850 - x = 850

680 +476 -x = 850

x = 1156 - 850

x = 306.

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Reject a null hypothesis because computed t is higher than 2.821 is the decision rule.

For the given question;

Test hypothesis:

H₀; μ = 3.5

Upper tailed test:

Hₐ; μ > 3.5

Significance value; α = 10.

Then, degree of freedom.

Df = α - 1

Df = 10 - 1

Df = 9

The critical value;

t(₀.₀₁, ₉) = 2.821

Rejection region;

Rejected H₀ for t > 2.821

Thus, reject a null hypothesis because computed t is higher than 2.821 is the decision rule for the absorption amount of the sponge.

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Step-by-step explanation:

In Peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses?

with glasses: x
without glasses: 3x

x + 3x = 28

4x = 28

x = 7 with glasses

7 * 3 = 21 without glasses

The equation of given graph is y = |x - 3| + 5.

The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.

Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.

As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.

So, by putting the value of vertex in general equation we get the equation of the graph,

y = |x - 3| + 5

Therefore, the equation of given graph is y = |x - 3| + 5.

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Brian has  £63 Initially, by using the ratio and proportion method.

What are Ratio and Proportion?

In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.

An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".

In the question, It is given that:

The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.

Let 7x denotes the amount in Brian's wallet and 2x denote the amount in  Colin's wallet on that day.

we know that:

Brian spent £39 that day.

Amount left in Brian's wallet = 7x- 39

Brian now had £4 less than Colin.

⇒ 2x -4= 7x- 39

⇒  7x-2x=4+39

⇒  5x=35

⇒  x=7   [Divide both sides by 5 ]

So , The initial amount in Brian's wallet  = 7(7)= £49

The initial amount in Colin's wallet = 2(7)= £14

The amount they had together =  £49+£14 = £63

So, They had £63 altogether initially.

Therefore, Brian has  £63 Initially.

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Answer: £14

Answer:

y = [tex]\frac{2}{3}[/tex] x - 6

Step-by-step explanation:

y - [tex]\frac{2}{3}[/tex] x = - 6 ( isolate y by adding [tex]\frac{2}{3}[/tex] x to both sides )

y = [tex]\frac{2}{3}[/tex] x - 6

The coefficient of the third term in the given expression is -4

From the question, we are to determine the coefficient of the third term in the given expression.

A coefficient is the numerical value that is written along with a variable or it is multiplied by the variable.

The given expression is

5 – 2t3 – 4t3u3 + 8v

This can be properly written as

5 - 2t³ - 4t³u³ + 8v

The third term in this expression is - 4t³u³

In this term, the numerical value that is written along with the variable is -4

Hence, the coefficient is -4

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Answer:

x = 16

Step-by-step explanation:

1: Put the numbers into an equation.

(1672.50 - 1068.50) / 37.75x

2: Solve the equation in parentheses.

(604) / 37.75x

3: Divide.

16 = x

Only 16 players can be brought to the tournament

The t-statistic for this hypothesis test will be 1.50 as "the average flight time for the pilots is found to be 8.12 hours. the standard deviation reported by the faa is 0.72 hours, and there were 81 pilots in the sample."

A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data match the distribution predicted by the statistical test's null hypothesis.

Here,

test statistic t is,

t = (x' - μ)/(σ/√n)

x'=8.12 hours

μ=8 hours

σ=0.72 hours

n=81 pilot

t=(8.12-8)/0.72/(√81)

=0.12/0.08

t=1.5

For this hypothesis test, the t-statistic will be 1.50 as "The pilots' average flight time was found to be 8.12 hours. There were 81 pilots in the sample, and the faa reported a standard deviation of 0.72 hours."

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A(n) Control Chart is a scatter chart with time on the horizontal axis, measurement scale on the vertical axis, displays mean and control limits, and may mark two standard deviations from the mean.

A control chart is one of the process improvement techniques or simply it is a graph to study how a process changes over time. In layman's terms the control chart shows if a process is under control or out of control. For calculating the average, there is always a central line in the control chart, an upper line and a lower line for upper control limit and lower control limit respectively.

The control charts are used to serve many purposes including monitoring a process for special variations and their causes and to remove them, estimating the process average and the variation, predicting the impacts of the process , etc.

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If Otis made [tex]1\frac{3}{5}[/tex]  cups of oatmeal and he put 2/3 cup of oatmeal into each bowl, then he made 12/5 bowls of oatmeal

Total quantity of oatmeal that Otis made = [tex]1\frac{3}{5}[/tex]  cups of oatmeal

Convert mixed fraction to simple fraction

[tex]1\frac{3}{5}[/tex]  cups = 8/5 cups

The quantity of oatmeal in each bowls =  2/3  cup of oatmeal

Then the number of bowls of oatmeal that he made = Total quantity of oatmeal that Otis made ÷ The quantity of oatmeal in each bowls

Substitute the values in the equation

The number of bowls of oatmeal that he made = 8/5 ÷ 2/3

= 8/5 × 3/2

= 12/5 bowls

Hence, if Otis made [tex]1\frac{3}{5}[/tex]  cups of oatmeal and he put 2/3 cup of oatmeal into each bowl, then he made 12/5 bowls of oatmeal

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Using the properties of arithmetic mean and average we get the value of 'w' is 22.

We know that mean is calculated by dividing the sum by the frequency.

Here n= 3

Sum = 5+6+7+w = 18+w

Now , (18+w )/4 = 10 which is the mean

or, 18 + w = 40

or, w = 40 - 18

or, w = 22

The value of w is 22.

By adding together all the observations and then dividing the sum by the same total sample sizes, the arithmetic mean of the supplied data can be calculated.

In order to determine the data's central tendency, an arithmetic mean formula computes the mean, or average, of the numbers. It can alternatively be described as the total number of observations multiplied by the sum of all the observations that were provided.

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Maggie's age is less than or equal to 11, m ≤ 11

An inequality can simply be described as a relation that makes an unequal comparison between two objects, numbers, elements or mathematical expressions.

It is used to compare numbers on the number line on the basis of their sizes

From the information given, we have that;

Let's substitute the values

5m + 4 + m ≤ 70

Now, let's collect like terms

6m ≤ 70 - 4

Subtract like terms

6m ≤ 66

Make 'x' the subject of formula by dividing both sides by its coefficient

m ≤ 66/ 6

m ≤ 11

Hence, the value is m ≤ 11

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Applying the distributive property, the given radical expression can be represented by 15.

The properties of multiplication are:

The question gives [tex](3+\sqrt{6} )(3-\sqrt {6} )[/tex]. Therefore, you should analyze the properties presented previously, and after that, you should identify which was used.

Here, it is possible to see that you can apply the distributive property. See below.

[tex](3+\sqrt{6} )(3-\sqrt {6} )\\ 9-3\sqrt {6} +3\sqrt {6}+6[/tex]

9+0+6=15

Then,  the radical expression (3+√6)(3-√6)=15

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The value of the car when she first purchased is $25001.73

Given,

current value of car =$18701.30

rate of depreciation annually=7%

time period =4 years

let the value of car when she first purchased be'x'

To find the value of car when she first purchased when it depreciated exponentially at constant rate ,use formula,

[tex]a(1-\frac{r}{100})^t=b[/tex]

Where,

a=value of car when she purchased

r=rate of depreciation annually

t=time period

b=current value of car

[tex]x(1-\frac{7}{100})^4=18701.30\\\\x(1-0.07)^4=18701.30\\\\x(0.93)^4=18701.30\\\\x(0.748)=18701.30\\\\x=\frac{18701.30}{0.748}\\\\x=25001.73[/tex]

Thus, the value of the car when she first purchased is $25001.73

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We're given :
Patricia originally has $3425.82 in her account.

After that, she deposits $9120.75, meaning her amount in her account goes up by $9120.75

Lastly, she withdraws $185.90, meaning her amount in her account goes down by $185.90.

Therefore, after the transactions, she has a total of : 3425.82 + 9120.75 - 185.90 = $12360.67

For the given triangle JKL, the value of x is 10. An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint.

Given information:

In  ∠J K L,JL is extended through point L to point M.

[tex]$&m \angle J K L=(2 x+14)^{\circ} \\[/tex]

[tex]$&m \angle L J K=(3 x+15)^{\circ} \\[/tex]

[tex]$&m \angle K L M=(7 x+9)^{\circ}[/tex]

See the attached figure.

At point L, the measure of angle JLK will be as,

[tex]$&m \angle J L K=180-m \angle K L M=180-7 x-9 \\[/tex]

[tex]$&=(171-7 x)^{\circ}[/tex]

Now, in triangle JKL, use the angle sum property to find the value of x as,

[tex]$$m \angle J K L+m \angle L J K+m \angle J L K=180[/tex]

[tex]$$$(2 x+14)^{\circ}+(3 x+15)^{\circ}+(171-7 x)^{\circ}=180$[/tex]

-2 x+200=180

2 x=20

x=10

Therefore, the value of x for the given triangle JKL is 10.

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The three valid congruency statements are; Triangle PQR = Triangle STU

Angles who are of same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of same measure, then

[tex]m\angle A = m\angle B[/tex] is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

Congruence statement states that a statement used in geometry that simply says that two objects are congruent, or has the  same shape and size.

Also, we can make congruence statements in words or in symbols. Using symbols we use the congruence symbol i,e  ≅ to indicate that two objects are congruent.

In the given triangles;

Angle T = Angle Q

QR = ST

TU = PQ

Triangle PQR = Triangle STU reason=ASA

Therefore, the three valid congruency statements are;

Triangle PQR = Triangle STU

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Answer:

Step-by-step explanation:

Answer:Yes, because the line that represents the first wall has a slope of -.25 and the line that represents the second wall has a slope of 4

Step-by-step explanation:

check the slope of both points

(-6,11.5) to (2, 9.5)  

11.5-9.5= 2

-6-2=-8

2/-8

m=-1/4

(-1, -2.5) to (2,9.5)

-2.5=9.5=-12

-1-2=3

-12/-3

m=4

Yes, because the line that represents the first wall has a slope of -.25 and the line that represents the second wall has a slope of 4