The total number of participants who went on the seventh-grade field trip to the Pink Palace consisted of all of the seventh-grade students and 19 adult chaperones. Two-thirds of the total participants rode a large bus, and the rest rode a smaller bus. If 104 people rode the larger bus, how many students went on the field trip? Write your answer below as a single integer.

Answer:

a=100, c=44

Step-by-step explanation:

# of adult tickets is represented by a

# of child tickets is represented by c

C+A=144

9a+6c=1164

system of equations is solved by solving 1 equation for 1 variable first.

c=144-a

plug in c in the second equation

9a+6(144-a)=1164

9a+864-6a=1164

combine like terms

3a=300

a=300/3

a=100

now we know a is 100 we can plug it into the original equation of c=a=144

c+100=144

c=144-100

c=44

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 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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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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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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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)

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

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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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

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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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 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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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

a) In any given experiment or trial, there is a probability that either an event occurs or it does not. The probability of the occurrence of an event lies between 0 and 1.

The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. However if the outcome ω is such that, ω ∉ E we say that the event has not occurred.

Let us take the example of playing cards. Here the event E is drawing a face card. If you draw a king of spades, we say the event E has occurred. However, if you draw an eight of clubs, we say the event E has not occurred.

b)  The probability of an event is equal to the events relative frequency in the population of possible events that can occur.

An event’s relative frequency is a number between 0 and 1, so the event’s probability is from 0 to 1.

For example, when someone says that the probability it raining today is high, you understand that they mean that there is a high chance that it will rain.

But what if someone says that the probability of something happening is very low? You understand that the person means that the event may not occur at all. In mathematics, we define probability in a similar sense.

What is Probability?

Probability is the measure of uncertainty of any event (any phenomenon happened or bound to happen).

What is event?

In probability, the set of outcomes from an experiment is known as an Event.

What is random events?

An event with a probability of occurrence determined by some probability distribution.

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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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Answer: (X^3)*y

:) Hope this helps, I spent a lot of time on it!

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

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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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

We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.

Given that,

The linear equation is y=-9x-10.

We have to fill the table given in the question.

First,

Taking x value is -8

We get y value as,

y=-9(-8)-10      (multiply -9 and -8)

y=72-10           (Subtracting 72 and 10)

y=62

When x is -8 y is 62.

Taking y value is -73

We get x value as,

-73=-9x-10

-73+10=-9x

-63=-9x

63=9x

x=63/9

x=7

When y is -73 x is 7.

Taking x value is 3.

We get y value as,

y=-9(3)-10

y=-27-10

y=-37

When x is 3 y is -37.

Therefore, We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.

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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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The graph of the function f(z) = - 0.25z + 4 is drawn.

Drawing the graph (curve) of the appropriate function is the process of graphing a function. Although graphing simple functions like linear, quadratic, cubic, etc. is very straightforward, complicated functions like rational, logarithmic, etc. need some expertise and an understanding of certain mathematical principles.

Drawing a function's representation as a curve on a coordinate plane is known as graphing. Every point on a curve (or graph) that represents a function satisfies the function equation.

A collection of edges that are ordered pairings of vertices (also known as directed edges, directed links, directed lines, arrows, or arcs) is displayed

The graph of the function is drawn. On the x-axis, the z-variable variables and on the y-axis the f(z) values are shown.

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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 number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

A permutation is an act of putting things or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.

Given that soccer player = 11

We have to find in many ways we can choose a captain and one alternate captain from a team of eleven soccer players

Out of 11 player, we have to pick one captain and one alternate captain

nCr ways

nCr = n!/r!(n-r)!

Here n = 11 and r = 2

= 11C2

= 11!/2!(11-2)!

= 11! / 2!.9!

= ((11x 10 x 9!)/2!.9!)

= (11 x 10)/2

= 110/2

= 55

Therefore the number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55

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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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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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